It sounds like a good tactic. I couldn't personally use it here, because I'm writing in our den, and my wife may be watching TV or reading, and that would be distracting to her.
At this point, the any proofreading is only opportunistic. Once all revision is complete, I then run the novel through my proofreading app. It splits the novel into discreet sentences, then presents them to me one sentence at a time in random order. When you mention your eye glossing over a wrong word, that typically happens when you proof the work straight through. You wind up reading the story rather than concentrating on the words, and read over mistakes.
Examining one sentence at a time, and in no particular order, eliminates that problem. In a list below, I display the sentence in context just in case that's useful, and it sometimes is. Over time I've added several points of analysis, and I display warnings for things like homonyms, clichés, copulas, overworked words, filler words, etc.
After one pass through every sentence, the app bumps a proofreading revision number, and then repeats the process with only the sentences revised in the first pass. That's because it's quite likely to introduce a new error as you fix another one. The revision passes continue until no revised sentences remain. Typically, each of my own passes is about 10% of the number of sentences from the previous pass. Those aren't all because I introduced another error ... most often it's just continued fiddling with a sentence I didn't like the first time around. By the time that's done, it's pretty solid.
Years ago I read somewhere that NY houses find approximately 7 typos in a full length novel to be acceptable after editing. I'm looking to beat that standard by the time I have a finished product.
I use headphones.
It seems like a combination of our techniques could be beneficial. One thing that reading and listening through the work catches (for me) is overused words.
What app are you using - I may look into picking it up.