An update:

1. Oiling slows the rusting, but does not eliminate it.

2. I've confirmed the celluloid scales degradation. I placed a piece of pHydrion paper between scales and blade where the rusting reappears, and the paper turned cherry pink (acid) over one to two weeks.

3. I've soaked the razor in 1% sodium bicarbonate to eliminate residual acid. This is probably not going to make a difference in the long term, but it's apparently controlled the problem in the short term.

I have yet to decide whether to salvage the blade with some new scales, or sacrifice the whole razor to experimentation.

This does suggest you might want to keep an open dish of bicarbonate of soda in whatever closed container you keep razors in, if any have celluloid scales.