Reading like an editor
Three passes, each with one job, none of them about grammar.
Editing your own draft fails when you try to fix everything at once. Split it into passes and each one gets easy.
Pass one: the argument
Read only the first sentence of every paragraph. If the piece still makes sense, the structure holds. If it does not, no amount of line editing will save it.
Pass two: the cuts
Delete anything you would skip while reading someone else’s draft. You already know which paragraphs those are.
Pass three: the sound
Read it aloud. Every sentence you stumble on is a sentence the reader will stumble on silently.