It's the upper seal between the plughole and bath, I'm guessing the Plumbers Mate wouldn't stain the inside on the bath, and even if it does, it'll be covered by the plughole but would movement from the bath as you get in and out or fill it for a bath not cause the Plumbers Mate to leak over time?
I'm not a plumber despite my forum name (messed up the signup
process, thought there would be a separate display name option later).
It doesn't stain and it really isn't visible once everything is tightened down and cleaned up. Plumbers made those waste seals, top and bottom for decades past. It's one of those cases where the "old way" is still a very good way. It really is the solution to your problem I think and it's what I would do if you asked me to come and fix this.