Specifying a structure's generation per dimension

I have a dimension full of vanilla ocean biomes, and need to move some vanilla structures like ocean monuments to spawn in that dimension and not the overworld. I've tried to deactivate vanilla ocean monument spawns and replace them with my own copy of them, but foolishly forgot that those copies would also have to use some equivalent to has_structure so ultimately the copies spawned in both as well. I also tried to create copies of vanilla ocean biomes but just attached them to a different namespace so they'd be 'different' and I could specify that way, but I was running into strange crashes upon entering the dimension I couldn't seem to solve. My question now is if I can simply use something similar to a has_structure tag but specify what dimension I want it to be in, alongside the biome. I'm not sure if you can put dimensions into the values though, so I'm a bit stuck.