I took everything apart and sanded down the pieces, then applied two coats of Minwax's "Special Walnut" wood stain. I wasn't trying to go for a totally different color, I just wanted to cover up the scratches and make it look better. (Despite there being no rain in the forecast, it started raining a few hours after I finished staining all the wood. While my cabinet doors were still outside. There may have been sobbing involved.)
A few days later, I applied three coats of semi-gloss polyurethane, then waited a few days to re-attach the handles and knobs. (I like the original hardware just fine, so I didn't care about replacing them.) There was no way I was risking sticky paint or, really, anything this time.
After the proper amount of dry time, Matt helped me reattach the doors, and the cabinets were officially done! They look so much nicer and sleeker! Renovation step one: complete! I declare it a success.
I did something right!!!!!!!!!!!!!