... One of the things I'm thinking is about undercutting the inlet and sort of dovetailing the ebony piece into the inlet. Kind of hard to put into words, but if done the way I envision it would have to slide forward to ever come out. I wonder if they were ever done that way, originally.(?) ...
Possibly misunderstanding your intent in the quote, but let me toss in my $0.02.
A cabinetmaker friend does a lot of inlay work - repairs, mostly - and some marquetry. From watching him work, talking it through with him and trying a little myself in his shop, the key to getting the tightest joints and no gaps is to not cut the inlay vertically. Rather, one cuts the inlay piece with a slight slope such that the exposed side is a bit larger than the side that will be glued to the substrate. Imagine, if you will, a stopper in a bottle. When you attach the inlay to the substrate, the exposed surface should be just a touch proud. Some careful sanding will bring it even and, because it was wider than the gap, bringing it even will result in there being no gaps at all.
I kinda doubt the ebony pieces were dovetailed into the inlet to keep them from falling out. Too hard to get the cut right and avoid gaps.