Are there any tricks to preventing the $3 plumbing pipe escutcheons from the
BORG from rusting after 2 months?

There is nothing more annoying than doing a nice paint job on a bathroom,
only to have the escutheon covering the toilet water supply rust.

I tried using shellac, and it only bought me about a month.

Would polyurethane or spray lacquer work?

I don't really want to invest any more than $3 on a simple thing, and I
don't understand why they make this crap so cheaply. Bathrooms are
_supposed_ to be moist.