Subfloor Problems Looking for A Solution
Not going to work the way your suggesting.
Adding screw to plywood patches that are not even T & G will do nothing to stop the flexing.
It's not that big a deal to cut out a subfloor and would be the best way to do it.
If for some reason your just not willing to do it a layer of 3/4 T & G Advantec that's screwed down, not nailed would be the next best thing.
Tile board has about 0 strength, would never stop the flexing, in fact it would just crack if it did flex, It's installed for a bonding surface for tile.