welcome to this community!!
1) Did I attempt to migrate a VM incorrectly?
Its correct. The issue here is VDR didnt delete the snapshot properly. its a known issue in vDR 1.0 and resolved in 1.0.1. what's the vDR version you are using?
2) Should I be able to migrate a VM on a system that is being backed up with VDR?
Yes, you can.
3) Is there any harm in deleting the "__data recovery__" snapshots? (I assumed that VDR would just recreate them)
This snapshot shouldn't exist after a successful backup using VDR. Looks like its a product issue. Its better to contact if you are using the latest version of VDR (2.0) for backup.
4) What is the "proper" way to migrate a VM to another VMFS volume that is being backed up by VDR?
As you've tried, storage motion is the best way to migrate the VMs across datastores.