It's certainly not the most ideal application, largely because in BB90, upon removal you only really have access to the inner race of the bearing to use the tool on. Versus being able to firmly plant the tool on the outer race then give it a good "pop" and voila, it's removed. In this scenario there's a chance you could drive out the inner race while leaving the outer race intact. It's never happened to me but I could see it as a possibility. Good luck. Still before you start jamming oversized bearings in there, I think just installing some regular bearings and making sure it's all locked up correctly just to see if that works is a good idea. It's what I'd do even if I was pretty "sure" the problem lies elsewhere. Stuffing in oversized bearings is just going to make creating an even larger bore all the more inevitable I think. Good luck. Let us know how it all ends up.
Yes all of these issues trouble me, which is why I am appealing to the collective wisdom of WW's.
Interestingly Trek changed the design of their Sram BB recently. A new supplier and a higher quality bearing. But the drive side now includes an inner plastic sleeve/dust cover combo. I didn't like it the minute I saw it. It was with this new BB that I first noticed the problem. I re-installed the older version and there is less play. Still not right but a little better.
Another approach would be to simply obtain a supply of the older BB bearings and just run those and hope that the problem doesn't get much worse. If it gets really bad, then maybe move to the oversize bearings.
When we ride disc brakes the whole deal of braking is just like a leaving a fart. It happens and then it's over. Nothing planned and nothing to get nervous for.