Summary of the resolution for historical reference...
Within CommVault, I have multiple subclients for my VMware host backups. Each subclient backs up all servers within multiple, specific VMware Resource Groups and is configured to back up multiple virtual machines simultaneously (some subclients do two virtual servers at a time, some do four, and some do six).
Previously, all subclients were configured to use Transport Mode for VMware=Auto and all backups were using the NBD mode. After applying the most recent Microsoft and VMware patches three weeks ago, CommVault started trying to do backups using the Hot Add mode. My CommServer is also my proxy server and is configured with a single (VMware paravirtual) SCSI controller which allows for a maximum of 16 disks. The Hot Add backups of multiple subclients with multiple servers per subclient and multiple disks per server resulted in many more that 16 disks which resulted in VMware backup failures.
The solution was to modify each of the subclients to Transport Mode for VMware=NBD. Since making this change, backups of my virtual server have run both cleanly and faster than when it was attempting to use Hot Add.
Oddly, all the other problems I was experiencing (Aux Copy running slow or failing, content indexing running slow or failing, etc) have been resolved. I'm not sure how or why the transport mode for VMware backups would have such far reaching effects nonetheless, changing the transport mode on five subclients has made all the other problems evaporate.
In answer to my post: I'm still not sure what the best method is to deal with multiple failures. I think I got lucky that the first ticket I opened fixed all the issues I was experiencing.