No.
I think you’ve got the right idea on how to approach the problem, but there isn’t a reliable technique to resolve all the issues that a white BG introduces.
The reason an additive keyer works is because the greenscreen isn’t bright, it’s basically neutral gray. Overlit greenscreens cause the same problems as an all white screen. I started a whole thread on the matter, but the end result of the thread was “no good answer” despite a lot of great techniques being shared.