I am not a teacher as you know but i like to share. Your questions, at least parts of them, are worked out in detail in Patisambhidamagga. I read it long ago. There something like this is said (often in my own words and from memory):
People have different inclinations, different focus, different abilities, different capacities. For some they focus especially on anicca. They have most feeling for this. Others on dukkha and others on anatta. That is a matter of which powers or abilities are dominant in someone. This is something personal.
All three are called gateways to liberation. I remember that those in which wisdom faculty is dominant they are more inclined to contemplate on anatta, and they are liberated by the socalled “emptiness gateway to liberation”. Other persons have or faith or concentration as their dominant powers and their gateway to liberation is, resp. called: signless and uninclined (sometimes undirected or desireless) gateway to liberation
It is said: “a meditator who has been focusing on the theme of inconstancy (anicca) will first apprehend Nibbana as signless; one who has been focusing on the theme of stress (dukkha) will first apprehend it as undirected; one who has been focusing on the theme of not-self (anatta) will first apprehend it as emptiness”.
So, anicca, dukkha and anatta are here threated as 3 gateways to liberation. I believe this is not really worked out in the sutta’s, like many is not really worked out. That’s why commentaries are handy.
One enters a gateway like entering a door. That seems to be the function of anicca, dukkha and anatta as it is explained in Patisambidhamagga. As gateway it leads to dispassion. Dependend on the gateway one takes, one apprehends Nibbana first as the signless (connected to anicca nupassana) or as uninclined and desireless (connected to dukkha nupassana) or as emptiness (anatta nupassana). These are all aspect of the unconditioned, Nibbana. So, they arrive at the same.
AN4.49 makes also clear what the function is of anicca, dukkha, anatta and asubha. They are meant to remedy our usual distorted perception or vision on things as nicca, sukha, atta and subha. This is a matter of perception. How things are viewed at a certain moment while they are arising. Viewing with a perception of nicca, atta, subha, sukha happens all the time. If i see a cookie i see it as sukha. If i become ill and are afflicted about it, it shows i see health as nicca. If i see a woman i see nicca, sukha, subha and atta and a lot more
Nicca, subha, sukha and atta is a wrong kind of attending to things seen, heard, sensed, known. Ofcourse a wrong viewing. It is connected to the arising of defilements and increase of those arisen. So, that is like entering a wrong gateway. A wrong development of the mind. You know all this.
Patisambhidamagga also says there is no difference between anattanupassana and sunyatanupassana. Only in words but not in meaning. This is explicity stated. If you want i can give you the exact reference.
And it also teaches that Nibbana is ultimate sunyata or ultimate emptiness.
There are also somewhere sutta’s that teach that from contemplating anicca, the perception of anatta also stabilises. So they are also connected but Patisambhidamagga explains that persons have more feeling for one, but arrive at the same.
I have read especially ‘the treatise on voidness’ and ‘treatise on liberation’ of Patisambhidamagga with great interest. There is so much not explained in the sutta’s. And those works are great, i feel.
I believe it is said that this treatise is connected to Sariputta.