You could always try command picture hanging strips - I’ve had great success with stuff weighing more than 1 kg. They can theoretically hang up to 5.5 kg so you should be fine. Each time I got them off the wall without damaging the paint too so bonus for that.

Is it metallic? Specifically anything a strong magnet can attach to?

If so maybe a wall mount with several strong neodymium magnets and a lip on the bottom to lessen the chance of it falling would help?

It’s the kind of thing 3d printing is great for.

I don't have the plaque, but would a holder for decorative plates do the trick?

There's always velcro? Though you may not want to attach it directly to the wall because of paint, you could probably use it to attach something for hanging, to the back. I recently mounted a nearly 10lb, 48"x24" white board directly to a metal door with a single package of adhesive mounting velcro. It wasn't even intentional, I had a whole over-the-door hook plan worked out for its mounting holes, using the velcro to keep it level and from any movement, and it turned out to be plenty, shockingly strong enough.

It's actually got me super excited for more hanging of weird things, cause I've gotten pretty good with Command Hooks, etc, and often find them wanting... Literally tonight, though I can't prove the timeliness, had one fall off the wall, that wasn't holding anything heavier than its load, just an old walking stick. Eventually, they die, and it seems the newer adhesive quality has become subject to enshitification, but I may also be a cynical shite. (งツ)ว

On a side note, does anyone know why it's designated "USS"? Doesn't that mean "United States Ship"? Isn't the federation a kind of whole earth effort? I know that there's an actual US aircraft carrier with that name, but I thought space travel was nonpartisan.

You can see where the four screws that mounted the original are sticking out. What a pity they didn't put holes where there are meant to be holes.