Two things:
1. I do BIAB and regularly get 80-85% efficiency without much trouble. My two tricks: I do a mash rest and a "batch sparge" (dunk the bag in second pot, combine runnings from both for the boil). Also, I squeeze the bag after every rest. Well, my wife does, I hold it up.
I'm convinced that the tannin thing is a lie, and squeezing before sparging helps dry out the grain, which then re-soaks up clean water to pull more sugars out during the sparge rest, which then get squeezed out. My setup is a waaaay simple stove-top apartment thing, so how you integrate a good squeeze into your system may be different, but I think it helps efficiency a lot.
2. Why do you need higher efficiency? I get the idea that it's fun to try and get your system working at its peak, so if that's the goal then go for it. Still, at a homebrew scale you're likely not saving much $$ by increasing efficiency. Much more important IMO is getting a
consistent efficiency. As I was dialing in my current method, I saw efficiencies ranging from 60% - 85%. As you can imagine, that makes it difficult to write a recipe. A swing like that is enough to make a session beer come out at just over 7.5% abv... If you know what the efficiency of your system is and you can hit it within a few points regularly, I'd leave it alone and just brew.