I haven't had much luck with the oil finishes on some woods with
figure. When applied, sometimes the oils muddy the figure and darken
it to the point of making it hard to see.

Your key here is minimum penetration, as shown by your success with
mineral spirits. Try using a good laquer on a scrap of your wood,
sanded exactly as you have sanded and prepared your box and see how it
works. I'll bet you'll be pleasantly surprised.

To paraphrase an old saying and one of the long lost members or this
group, "practice finishing on a scrap or practice finishing on your
project... which one makes sense?"

This is great advice always, but with all the different kinds of wood
available to us now, it seems more timely than ever.

Robert