For the lemmy.ml comm: post a few times there, then post in c/community_requests that you want to mod that comm. Include a link to one of your posts in the battlestations comm, and info about its current mods (the same as you said here, that the mod is inactive).
For the lemmy.world community: I’d first demonstrate overall interest on the community by posting often there, and then ask the current mod; there’s a good chance that the mod mass created communities to promote the place, and wouldn’t mind if someone took one of them to nurture it. If the mod says “no” you could always leave it be, and create your own comm.