Screen readers doing OCR is a big no-no. There is no possible way that will have the effect you want it to have. The text-to-speech part is the absolute bare minimum of what a screen reader is actually doing. For example that would break horribly with the situation you describe, where some piece of text gets clipped.

Just IMO, it's unrealistic to expect to have an accessible GUI that stores no state, does none of that type of bookkeeping, has no OOP model, and only outputs to pixels. The point with these type of assistive technologies is that the user can't work with that type of visual data, they need more state presented to them. Sure, it makes everything easier to develop when you cut it all out and only use immediate mode, but that's exactly the problem: everything else has been cut out, on purpose.