You can't, indeed, live migrate a VM from Intel to AMD (or vice-versa), for obvious reason (the VM will try to call Intel specific instructions after migrating on an AMD CPU, the result would be… a crash!)
We had a similar migration ourselves (in our own prod), from Intel to AMD. And we decided to use Continuous Replication to make a first "backup" on destination (the full) while the original VMs were running (no service interruption).
Then, we shut down the VMs, make another round of replication (delta, very fast) and then we booted on destination.
