VMWare Backups of active VEs?

I have customers with the same issue as to different team maintaining certain infrastructure. Some chose to run dedicated hardware and not be subject to the whims and scheduling of another team within their organization. Not the answer you were looking to get, but certainly another option to consider ;)

FWIW I use a VMware workstation lab environment, and torture my F5 VE guests. I usually have no issues with rebuilding from a particular UCS when needed, even thought I pause, snapshot, etc. all the time. Also, keep in mind one other important thing.... to rebuild an F5 VE, you really need a few things --- the master password which you can obtain from the other unit and rekey on the replacement or target unit, and the base configuration. So, even if you base configuration is a bit old, as long as the F5 VE is serviceable, you can rebuild missing config (shared config only) by syncing from the surviving unit. So just some more ideas.

From experience using vsphere for lots of lab BIG-IPs, DB (MCP and REST both) problems do sometimes happen when you snapshot and do hard shutdowns. And the fact that the running-config isn't necessarily the same as the saved-config.

I'd expect that you could issue a "tmsh save sys config" to align the running-config and saved-config, then "bigstart stop" to quiesce the system and it'd be OK to move/snapshot. At that point, there shouldn't be any consequential open files. To recover you'd of course need to reboot or "bigstart start" the system.