Finished rubbing the frame down, dried it, dedgreased it, washed it, dried it again. This has let a fair bit of exposed steel that I don't want open to the air any longer than necessary, so I hung the frame up and blasted it with a coat of epoxy-anode zinc primer then left it hanging to dry. I'll snap a photo in the morning when the light's a bit better.
Aside from the corrosion resistance and the tough, hard physical barrier, it has 2 other advantages. It's high solids, so has filled any minor imperfections, and when I rub it back ready for paint primer it's going to be smooth as treacle hand poured by Barry White.
Second advantage is that this primer is silver, so it has given me a rough visual indication of how this frame is going to look in that colour when it is finished. And I can tell thee, it's great!