I don't know if I have any advice for you, Phylum, but maybe just a few background things you should know about multiple stores (that I learned from the school of hard Mirage knocks and VMware Support).
The first is that all app layers are local - meaning that any app layers that the CVDs contain have to be copied to the share first. You can see this happening in Task Monitoring.
The second is that app layer copy operations are very low priority. If there is anything else going on with that CVD store, app layer copies will take a back seat.
Somewhere in VMware documentation is a recommendation to move no more than 10 CVDs at a time.
Lastly, it's possible that the CVDs you move will become corrupted by the move. This is a good time to run a CVD Integrity check. This will restore app layer and CVD functionality.