I think I have the skipping issue sorted. It's going to take some more riding, but I'm pretty sure right now that the issue was with the front derailleur wasn't in quite the right position. I fiddled with it a bit this morning on my way in to work, and the trip there was skipless, as was my trip home tonight.
I'm not 100% sure, though, because when it was skipping it was on the middle chainring (new), and today I had it on the largest chainring. It's barely conceivable there's something wrong with the middle chainring, but I'm pretty sure I just need to get used to friction shifting again.