You'd actually end up with a 'split horizon' setup wherein LetsEncrypt (and the public) see those DNS names with the external gateway's IP and ping that for the validation files.
Your options at that point are a central 'well known' directory that different hosts can write to (I recommend sshfs), different directories on one host that are checked for any valid file in any of them (by default) or by hostname match in specific, etc. The details depend on your security model.
Your options at that point are a central 'well known' directory that different hosts can write to (I recommend sshfs), different directories on one host that are checked for any valid file in any of them (by default) or by hostname match in specific, etc. The details depend on your security model.