There isn't any early discourse that talks about "store house of kamma".
However, in a Pali early discourse, there is something called “stream of consciousness”, which is mentioned in DN 28 (its Chinese parallels, DA 18 and T 18, don’t use the term “stream of consciousness”; DA 18 just uses the word “consciousness”, while T 18 instead talks about a “defiled body”). Nevertheless, they talk about the same thing, which is, how some ascetics or brahmins know that a person’s consciousness, unbroken on both sides, is established in both this world and the next, and how it isn’t. Interestingly, DA 18 says that when consciousness isn’t established in both this world and the next, there’s a break on both sides. Since all three versions talk about some kind of continuity of consciousness, I think the term “stream of consciousness” in DN 28 makes perfect sense.
In Translitteration question def. Rebirth, Venerable Sujato explained the stream of consciousness like this:
I would phrase it rather as “actions have an ongoing influence on consciousness”. It’s true, some Buddhist traditions used the concept of a “storehouse” to explain this, but I don’t feel that’s the most useful metaphor. Better think of it like a stream: you dump pollution in a stream, it will make its toxic effects known downstream (i.e. later in this life or in future lives) until it’s either diluted or cleaned up.
There’s also the simile of a flame going out in MN 72/SA 962/SA 2 196. A burning fire depends on grass and logs as fuel; without grass and logs and fuel, the burning fire goes out. You can also think of the burning fire like this: when a fire burns from a starting point all the way to a far end point, you certainly can’t say that the fire from the starting point is the same as the fire from the far end point. The fire just burns continuously. There isn’t anything that can be called a self.
As for deeds (Kamma)'s place of origin, AN 6.63/MA 111/T 57 say that deeds come from choice/intention (Sankhara) since choice leads to either good deeds or/and bad deeds. AN 6.63 agrees with MA 111 that choice leads to deeds that lead to rebirth in hell, the animal realm, the ghost realm, the human world, and the world of the deities; while MA 111 agrees with T 57 that choice leads to dark deeds with dark results, bright deeds with bright results, dark and bright deeds with dark and bright results, and neither dark nor bright deeds with neither dark nor bright results, which lead to the ending of deeds. All three versions agree that the practice which leads to the cessation of deeds is The Noble Eightfold Path.
As for things that maintain deeds, I believe there are two angles that you can look from. The first angle comes from the angle of ignorance/delusion (Avijja). According to both SN 12.35/SA 297, ignorance/delusion is the very root of all suffering; when there is no ignorance/delusion, there is no suffering. The second angle comes from the angle of lust, anger, and confusion. According to both AN 10.76/SA 346, without giving up these three things you can’t give up rebirth, old age, and death. Rebirth, old age, and death will cease only when lust, anger, and confusion are given up. This is why Buddhas and perfected ones can no longer be reborn; any deed that is done by them is devoid of ignorance/delusion, or lust, anger, and confusion according to SN 11.3/EA 24.1/SA 981.
You said that:
There are certain teachers that state, with equanimity kamma (sankharas) are brought to the surface to be experienced as sensation and thereby purified and this “storehouse” of kamma is gradually eradicated.
this reminds me of both AN 10.219/MA 15. Both versions say that those (women or men) who develop the heart’s release through the holy abodes (Brahmavihara) which is comprised of: love, compassion, rejoicing, and equanimity won’t do any bad deed, and suffering won’t be able to afflict them. Since no one can take their body with them when they die, those who develop the heart’s release will understand that “whatever bad deeds I have done in the past with this deed-born body I will experience here. It will not follow me to my next life.” The development of the heart’s release can also lead to non-return (the holy abodes by themselves can’t lead to awakening, it must be paired with the insight on nonself as well). There’s one noteworthy difference between AN 10.219 and MA 15: AN 10.219 says that one’s deeds must be exhausted before making an end of suffering. MA 15, however, doesn’t say that at all; it instead says that unintentional actions don’t lead to any kind of deeds (unintentional actions are actions that aren’t influenced by lust, anger, and confusion).
The case of Venerable Angulimala is interesting. EA 38.6 and T 118 mention that the bandit Angulimala thinks about killing his own mother. MN 86, EA 38.6, T 118, and T 119 mention how Venerable Angulimala is attacked when he begs for food in a town, and how he helps a woman in labour deliver her baby. These stories are entirely absent in SA 1077 and SA2 16. That being said, there’s a line in Venerable Angulimala’s verses in MN 86, T 118, SA 1077, and SA2 16 where Venerable Angulimala says that his bad deeds should cause him to get a rebirth in a lower realm if it weren’t for his practice in the Buddha’s teachings. There’s also another line in Venerable Angulimala’s verses in MN 86, EA 38.6, T 118, and SA 1077 where Venerable Angulimala remarks that he has already experienced his deeds. These two particular verse lines may point to the narrative where Venerable Angulimala is attacked by a group of villagers. On the other hand, the narrative may simply be a result of later addition basing on these two verse lines.
There’s the story of Venerable Moggallana being killed because of his past deeds where he killed his parents in one of his previous lives; this story is commentarial, and it doesn’t occur in the early discourses, so you shouldn’t pay too much attention to this story.
Now, let’s say that Venerable Angulimala is indeed attacked by a group of villagers instead of being reborn in a bad realm, both AN 3.100/MA 11 can explain this situation. Both versions say that those who do trivial bad deeds but end up in hell is because they are not virtuous and wise, so they do little merit, and bad deeds outnumber good deeds; this is just like a lump of salt in a small bowl of water where the water is salty and undrinkable. Those who are virtuous and wise, however, will experience bad deeds in the present life without a bit left over or a lot even when the trivial bad deeds are the same as those who are not virtuous and wise. This is because those who are virtuous and wise do a lot of merit, so good deeds outnumber bad deeds, just like a lump of salt in the Ganges river where the water is still very much not salty and is drinkable.
Venerable Angulimala’s case can also be explained with both MN 136/MA 171. Both versions agree that those who make good deeds but get reborn in a lower realm is because they have wrong view later in their lives, while those who make bad deeds but get reborn in a good realm is because they have right view later in their lives. Dhammapada 172 and 173 with their parallels in other Indic languages say that those who were heedless/did bad deeds before but afterwards are heedful/do good deeds light up the world, like the moon freed from a cloud. Dhammapada 172 and its parallels appear as one of Venerable Angulimala’s verses in MN 86 and SA 1077, while Dhammapada 173 and its parallel appear as one of Venerable Angulimala’s verses in MN 86, EA 38.6, T 119, and SA2 16.
Anyone who is at least a follower by faith is forever freed from any rebirth in the lower realms, can’t die without realising the fruit of stream-entry, and will only get reborn in a good place in the human world, or in a heaven according to every discourse in the Okkanta Samyutta of the Pali Nikayas and SA 61 of the Samyukta Agamas (T.99).
When it comes to the workings of deeds, both AN 3.61/MA 13 say that the belief which everything is caused by past deeds, a creator God, or chance is wrong. SN 36.21/SA 977/SA2 211 say that not everything one experiences is caused by deeds; there are mundane things that cause us to experience different things in our lives as well. In the Pali Nikayas, AN 4.77 says that the results of deeds are inconceivable. While AN 4.77 doesn’t have any exact parallel discourse, it does have a similar discourse in the form of EA 29.6. EA 29.6 has a similar passage which says that the arising of beings is inconceivable; it’s not possible to know exactly where beings come from, where they go, where they arise, and where they get reborn after passing away.
Those who cannot redeem themselves in the present life are those who have done the following: killing one’s mother, killing one’s father, killing a perfected one, causing a schism in the community (I’m not sure whether “community” here refers only to those of the mendicants or if it refers to the entire four-fold community of the Buddha ), and injuring a Buddha with malicious intent. Anyone who has done any of these five grave deeds can no longer realise any stage of noblehood in the present life (like King Ajatasattu who kills his own father according to DN 2/DA 27/EA 43.7/T 22), and will definitely fall to a lower realm after death. In the Pali Nikayas, those who have done any five grave deeds will certainly fall to hell after death, but I can’t find that certainty in the Chinese Agamas. SA 792 (this discourse has no parallels) says that those who have committed any five grave deeds will be reborn in a lower realm. So, I’m not sure whether committing any five grave deeds will cause someone to be reborn only in hell, or if such action will cause someone to be reborn in any of the three lower realms (hell, the animal realm, and the ghost realm).
On the contrary, it is impossible for anyone who is at least a follower by faith to commit any of the five grave deeds according to MN 115/MA 181/T 776.