First off, don't migrate things to beta sites. Just don't.
Ok, if it's blatantly off-topic where it was asked, a shining example to the world of a bomb-ass question and you're 110% certain it'll be well-received where it lands... Yeah, just don't migrate to beta sites.
That out of the way... Generally, moderators shouldn't be the gate-keepers for a site. A well-run site with a thriving community will have a host of active users who can close, edit and comment, working to salvage any worthwhile questions that come their way. Of course, beta sites are not generally thriving communities with hosts of active, moderating users - see above...
With all that out of the way, all that's really needed to "fix" the current migration system is a message in the "off topic" banner on rejected questions noting the site where the close voters thought it was on-topic. Anything more complicated than that is a waste of effort, IMHO - only something like 60% of askers even follow their questions to the destination site anyway, and a much smaller number will ever put any effort into fixing them if they're closed.
Disclaimer: I'm stating a general policy here, guidance that should be followed in most situations - but if you know better in a specific case, then ignore it. That said, if you're not confident enough to migrate without asking a moderator on the destination site, you're not confident enough to ignore this guidance.