You are right that nobody reads two hundred papers end to end. The standard approach is to read almost all of them shallowly and a handful deeply, and to decide which is which deliberately.
Pass one, five minutes. Title, abstract, section headings, figures, conclusion. Then answer three questions in writing: what problem is this, what did they do, and is it relevant to me. Most papers stop here permanently, and that is the correct outcome - that is what the pass is for.
Pass two, half an hour. For the ones that survived. Read properly but skip the proofs and the fine detail of the method. Look hard at the figures, because that is where the actual result lives. You should now be able to summarise it to someone else.
Pass three, hours. For the small number you will build on or argue against. Reconstruct the work, question the assumptions, note what you would have done differently.
Of two hundred, you might expect something like a hundred and fifty at pass one, thirty at pass two, ten at pass three. That distribution is normal.
What you have been doing is attempting pass three on everything, which is why nine papers took months and why nothing stuck. Two hours per paper is a pass three cost applied to pass one material.