I just ran into the first rain I've seen in the mod, and I really like the actual rain blocks placed on the ground. Would it be possible to have this as a standalone mod for use in other dimensions?

You're in luck, this exists already ;)
https://minecraft.curseforge.com/projects/puddles

They're pretty much the same though, no? Ours just have some more thickness and a very slightly different texture.
You should be able to change the model and texture of those puddles yourself with a resource pack ;)
See Puddles block model, Creating a resource pack and Block models.

Sorry for the delay in reply, work sucks. I have looked at the mod mentioned and the puddles don't really fit with minecraft, and don't look nearly as nice as the ones from this mod.