So I've made some progress... I have finished priming the jewelry box. It took longer than expected, and is taking FOREVER to dry in this humidity, but it was worth all the effort because I think it's looking pretty good so far for an unfinished box!
I plan on next sanding it down a bit very lightly with a fine-grit sandpaper (around 220), then wiping off the dust with cheesecloth (found at any hardware store), and coating it with some latex paint. So far, so good!