In thinking about this & confronting the challenge myself this is what I think I’d do next…

In front of the lug at a location of your choosing, put down a tape barrier for a couple inches to capture the ‘forward overflow’

At the tape line junction, there will be a precise point where the bedding compound is no longer attached to the stock substrate & will be easier to trim back to that point with a razor knife skor.

I’ve not done this so I could be full of buckeye balls but I fully understand your question & have wondered about solutions myself.