Update -- since I started disabling the WinMgmt service before backups and re-enabling it after, I have not experienced this problem on any of our servers.
I do get a bunch of error messages in the System event log stating that DCOM tried to start WinMgmt but could not because it's disabled. These messages are logged while the job runs, and disappear afterwards. Unsightly, perhaps, but harmless (and certainly less important than having my backups work!)
Best of luck to all...