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It seemed easy, given that the NS records were preserved when transferring. I figured: this meant I could take my time in copying over the DNS records to somewhere new.
Wrong -- when my domains transferred, Google deleted all their associated DNS records.
Maybe my real mistake was letting Google manage my domains and DNS records. Forgive me for thinking that the largest web company would be the best place to do so.
I don't remember all the DNS records I threw onto my domains or where they came from. I restored the ones I remembered, but I'll surely notice things breaking over the next few days.
It might be an amateur mistake not to back-up all DNS records, but I'm sharing this so others don't make it as well.
It's not every day that you need to migrate registrars.