Hey, again! 
But also said to be experienced “with the kāya” are “the deathless”, “the formless states”, and so on. I think you’ll agree it doesn’t mean ‘with the body’ there.
Ah! That sutta is actually the best argument against “disembodied” jhanas, and I’m happy you brought it up. 
If this is what the Buddha himself said, then yes, it would be awkward to interpret this with one meaning of kāya as ‘experiencer’ and the other as ‘body’.
However, the jhanas fit very poorly into the overall sutta. I explained it in some length in this other topic. Consider for example:
“After you get fully separated from sensual experiences and unskillful states of mind, you attain the first jhana […] As you meditate like this, being diligent, motivated, and energetic, you will abandon worldly memories and intentions [i.e. the hindrances]. Once they are abandoned, your mind gets fixed, settles down, reaches oneness, and unifies internally.”
This say that you abandon the hindrances and attain the first jhana, after which as a result you abandon the hindrances and attain the first jhana. That makes no sense. Something is off here.
I think the passage of the jhanas is inauthentic and only included because of the word kāya. The more authentic version of mindfulness of the body is taught in the Satipatthana Sutta, where the jhanas are missing.
The similes for the jhanas (which speak about “the kāya (experience) filled with pīti”) are quite rare in the canon. They occur in DN2, MN39, and MN77, the Chinese parallels of which ALL lack the similes! Clearly the Theravada tradition had a tendency to add these similes to suttas which originally didn’t have them.
They are also in MN119, the sutta you’re referring to. But here it is also different from the Chinese. Because in the Chinese the jhana similes are included but the jhanas themselves are not. Strange. Again, it’s inconsistent and broken.
The last instance in the Pali canon is AN5.28, which to me seems the only authentic discourse with these similes, and it’s no surprise that it’s the shortest of all of them. Now interestingly, this text has three similes on “able to realize” which are found only here and in MN119. A coincidence? I don’t think so. I think, although we can never be sure, that MN119 is an “accidental” mix of the Satipatthana section on mindfulness of the body together with AN5.28. It was done by somebody else than the Buddha.
It could have been done on purpose as well. Scholars agree that the Pali texts have been edited, and one of the clearest aspects of editing is this sort of thing, where passages are linked together in inauthentic ways. We can derive this from comparing the Pali to the Chinese, for example. It happens quite a lot, especially in the longer texts like DN and MN. Normally such inauthentic inclusions don’t create any problems, so we almost never notice them, but in MN119 they do cause an issue.
See also Ven. Sujato’s “history of mindfulness”. It doesn’t address MN119 as far as I recall, but it does show some of these principles with respect to the Satipatthana sutta.
Yes, you have a good point, but study how ill the jhanas fit into the sutta, and you may see it from my perspective.