How do I patch a hole around a shower valve when the trim plate is way too small?

I've done almost exactly this patch job on an old one-piece tub surround after a valve swap left me with a hole way too big for the trim plate. Your PVC/acrylic plate idea is the right one, and it held up fine for me for years. Skip the epoxy putty route, it's miserable to tool into a big ring shape, it doesn't bond great to glossy fiberglass, and it'll crack off the first time anything flexes behind it.

What I did was grab a scrap of 1/8 inch PVC sheet from the big box store, but honestly a piece of FRP panel or even a flat plastic cutting board works if that's what you've got lying around. Cut it big enough that it overlaps solid surround on all sides by an inch or more, then cut the center hole just big enough for the valve body to pass through. The escutcheon will end up covering the seam between the plate and the hole, so it doesn't need to be pretty. A hole saw or a jigsaw with a fine blade handles the center cut. For bonding, 100% silicone is your friend here. Scuff the back of the plate and the surround around the hole lightly with sandpaper, wipe both down with rubbing alcohol, and lay a generous bead of silicone on the back of the plate before pressing it on. Silicone grabs fiberglass and plastic great, and unlike construction adhesive or epoxy it stays a little flexible, which matters when the wall moves and things get soaked. Once the silicone has cured for a day, run a good bead around the outside edge of the plate where it meets the surround, and another where the escutcheon meets the plate. Tool it in with a wet finger. If you want to be extra sure, put a bead inside the center hole too before the trim goes on, so water that gets behind the escutcheon hits silicone instead of raw wall cavity.

Since it's a basement shower and looks don't matter, that's the whole job. One afternoon and a tube of caulk.

I'd push back on the silicone-as-glue part. It's a sealant first, and on smooth plastic it tends to peel off in one piece when you test it, which is exactly what mine did. The scuff and alcohol wipe helps but it's still not a real bond on acrylic sheet. I screwed my patch plate into the surround with a few plastic-cored washers and stainless screws into the studs behind, then caulked over the screw heads. The caulk only has to seal, not hold anything up. Basement walls flex and get soaked, and a plate held up by silicone alone is one good bump from a mop handle away from popping loose.

Before you cut a plate, check a plumbing supply house for an oversize escutcheon. I was mid-project cutting a patch out of sheet plastic when the guy at the counter asked what I was making, then handed me a universal escutcheon plate, basicly a big chrome disc with a smaller hole pattern and a rubber gasket behind it. Covered my oversized hole with zero fabrication. They're cheap and they exist for exactly this mess after a valve swap. Not every hardware store stocks them so call around, but a real plumbing supply usually has them in the trim drawer. Might save you an afternoon.

One thing to watch with the plate method is depth. When I did this on my own basement shower the new valve body sat about half an inch further out than the old one, so my patch plate ended up riding proud of the surround. The escutcheon still covered everything but the handle nearly bottomed out against it. Dry fit the plate and screw the trim on before you commit to any glue, and make the center hole snug so the trim plate actually clamps the patch down when you tighten it. That way the plate is held by the valve itself and the silicone is only doing sealing duty, not structural work.

Update: the supply house thing saved me, they had the universal escutcheon and it covers the whole hole with maybe a hair of daylight left around it, so no patch plate needed. But that depth comment got me thinking, my new valve does sit a bit proud and the escutcheon wobbles out from the wall. Can I just put a bead of silicone behind it and squish it til it sits flat, or does that trap water where I can't see it?