Import form submissions from one site into another

[modelesque]

I created a massive form on a client's temporary site while working on the full refresh on a staging server. While that development's been going on, the live temp site has been collecting form submissions the whole time. We're preparing to overwrite the live server with staging's db, and the only thing that needs to be conserved from the live temp site is all those form submissions that came in. Does anybody know a solution on how to do this? I've purchased Verbb's Feed Me plugin but unfortunately it doesn't include importing to custom element types.