Using the original TeX source for the screen reader is significantly hindered by the fact that TeX isn't a markup-, but a programming language.
TeX is turing-complete by design, making it infinitely extensible, in order to avoid knuth ever having to re-typeset his books. After all if it's a programming language and a new system, problem, style, e.t.c, comes along you can just write a program that deals with it.
But this has horrible effects on render-ability, in order to know what the final document should look like, you need to run it, no way around that, thanks to Rice's theorem.
LaTeX users also generate a lot of their figures with TeX itself, write their own styling or bibliography rules, and write their own custom graphics rendering libraries.
The easiest path is to just give up, render the entire PDF to a 300dpi lossless image, and throw it into an OCR engine. These things contain a buttload of heuristics to generate structure and meaningful text based on visuals, and since we know that humans explicitly (and often only) care about those in TeX documents...
It's pretty darn sad, because in many ways TeX is holding scientific advances back, by eating its own children. My guess is that if scientific papers had branched off of plaintext tools like troff, we'd probably publish papers as machine readable semantically annotated knowledge-graphs by now.