My method for box lid cutoffs is to cut the long sides through with the blade set as high as one feels comfortable, but not high enough to also sever the ends.
I then lower the blade to cut 90% of the way through the ends. This leaves a thin section which can be cut with an Exacto knife, working from the inside out (avoids chipout).
This avoids the worries about blade pinching.
One can also use 1/8" aluminum angle shims that can be slipped into the through cuts and securely taped to the box surface.