AXFR isn't the only way to sync records between providers. You just need a tool that speaks to the APIs of each provider and can sync between them that way. Heck, I had syncing in place at a startup between Route 53, DNS Made Easy, a pair of TinyDNS servers, and a git repo (which was our historical backup of changes) years ago. It was 300 lines of Python and 100 lines of shell. Albeit, we only had a few dozen or so records to manage, but this isn't rocket science.
Aside: I came out of college as a sys admin with a CS degree and writing tools like this was par for the course. If devops folks aren't writing tools like this today, what are they doing?
Honestly: I think they are spending most of their time moving existing working infrastructure into containerized infrastructure and figuring out how to deploy their blog on k8s. They are working on learning libraries that abstract abstractions.
Aside: I came out of college as a sys admin with a CS degree and writing tools like this was par for the course. If devops folks aren't writing tools like this today, what are they doing?