To follow up, I ended up removing as much of the surface rust as possible, then I used clear nail polish over those areas.
Here's a photo of the bike, just completed today:
IMG_20240304_163817758 by
warren t., on Flickr
The only original parts are: the headset (I installed new loose ball bearings), shift levers (Suntour Power Ratchet), front derailleur (Suntour Cyclone), and pedals (SR).