Thanks for the feedback. Is it possible that removing the rust with something like naval jelly will leave a cavity in the surface of the plastic? I.e. has the rust displaced some of the plastic? I'll test it first on the inside surface that's covered by the buttplate, as you recommended. I think I'd prefer to live with the stains rather than end up with pitting or an indentation on the surface.
Edit: I just read a couple reviews that said that naval jelly is not recommended for use on nonferrous materials such as plastic. I found this article on Bob Vila's website that lists Evapo-Rust and CLR PRO Calcium, Lime & Rust Remover as safe on plastics:
The Best Rust Removers for Household UseSounds like Evapo-Rust might be one to try: "It’s also safe to use on non-rusty steel, plastics, PVC, cast iron cookware, toys, and most painted surfaces that may be in contact with rusty metal hardware."
The CLR Pro Cleaner section says "The formula utilizes both lactic and gluconic acids, which are less caustic but no less effective than harsher acid-based removers. It works wonders on rusty tools, outdoor equipment, car parts, stainless steel, plastic, ceramic tile, glass, and fiberglass surfaces and is also a great alternative to ammonia- and bleach-based products on hard water deposits, soap scum, and rusted toilets."
I'll look into those two options. Not sure how I missed that article the first time around.