Hi Nickelii, welcome and thanks for joining the discussion.
When I read the sutta, it seems clear the further escape for each state is every time the next state of meditation. The escape from the first jhana is the second jhana, the third is the escape of the second, and so forth. The final escape is the cessation of awareness and what is experienced (or “perception and feelings”), after which Sāriputta concluded there is no further escape. This cessation of awareness and what is experienced is a momentary version of parinibbana, the cessation of the mind, that’s why he couldn’t find any further escape. Because there’s nothing else to cease.
You say contemplation in the jhanas, well, this moves the discussion from whether the jhanas are bodily or mental, to the question of whether one can contemplate in the jhanas. I don’t feel like going there now in much detail, but Ven. Ānalayo argued that this sutta (MN111) does not support the idea that one can contemplate in the jhanas (in Early Buddhist Meditation Studies.) One indication is that before the contemplation the sutta says: “He [Sāriputta] knew those phenomena as they arose, as they remained, and as they went away.” In other words, he experienced the jhana and its ending, and only then contemplated it. Only then “he understood: ‘So it seems that these phenomena, not having been, come to be; and having come to be, they flit away.’”
We have to read the sutta as a general description of Sāriputta’s practice, not as something he did in one single sitting. After all, the sutta starts with “for a fortnight he practiced”. During that time he still went on almsround and ate and stuff, surely, but that’s sort of thing is left mentioned since it’s irrelevant. It’s also irrelevant to mention that Sāriputta had to attain the first jhana again before moving on to the second.
So what happened is, Sariputta attained the first jhana (perhaps a couple times), contemplated it, realized its limits, then developed the second jhana, for which he needed to go through the first again. As it says, he realized these things “by repeated practice”. So it wasn’t 1st jhana > contemplate > 2nd jhana > contemplate > 3rd jhana, and so forth. It was more like, 1st jhana > come out of 1st jhana > contemplate > 1st jhana again > come out again > contemplate again > 1st jhana again > 2nd jhana > come out of 2nd jhana > contemplate > etc.
For example, the 2nd jhana is a further escape from the 1st jhana, and “by repeated practice” Sāriputta realized that. But only after the cessation of awareness (saññā) and what’s experienced (vedayita) did he realize that there is no further escape.
(This is another indication, by the way, that saññā can just mean awareness in general, and not always means mental labels or ideas, which is relevant to kāmasaññā we discussed earlier.)
The discourse also has some clear indications of lateness and Abhidhamma influences, but that’s yet another matter.