Make passes into a game. Rush through at speed. If you are really stuck on a sentence then skip it, the same way you do as drafting. Sounds counterproductive, right? But I frequently encounter the same thing, and I'll do a dozen passes on an MS no matter how much nitpicking I do with each pass.
I usually start with pulling out my notebook for a story, and I start on a fresh page, and outline the story with ink as I go through it. My first couple of passes are focused completely on the story, and the notebook helps me keep up the pace. My first "edit" in fact, is nothing more than a note-taking read-through. Going fast helps me spot big plot holes and overall changes that need to be made to characters when they are acting "out of character." On that pass, faster is better, and I only fix easy, glaring issues.
My second pass targets the spots I've identified, and I work toward making the story consistent and seamless. This is also when I rip up unnecessary scenes and add needed ones. I move whole blocks of text, even chapters. Then I do another story pass at reading speed to see if everything I've done is working.
Once the big stuff is out of the way, I do 2 or 3 quick passes fixing sentences. As I said, if I can't fix it in five minutes, I move on, telling myself that I'll catch it on the next pass. Stories are always messy at first, but instead of making every single paragraph perfect, I focus on fixing what I can without wrecking my brain when I can't come up with a good verb.
This iterative process makes the story better and easier to read with each pass, freeing my brain up to be more fresh when I come back to the hard sentences, and they don't seem as difficult the next time around. It also keeps me actively involved in the story. I should be able to finish at least a chapter per day on each editing pass, and I work on other stories in between.
Another thing I notice is that I'll get better at editing with each pass. Just like writing, editing is a skill that develops a little more every time you go through a story. Looking up I see that some others have hinted at this, too. Maybe there's a nugget here that can help further though.