I maintain data and data history (Safety Net) via Carbon Copy Cloner. I treat my TimeMachine backups as snap shots in time of the most recent installation. I have no use for history associated with TimeMachine, so reformatting a TM drive is no big deal. TM is rather limited and seems cobbled together to me, hence my solution to use CCC. And since I have all Intel Macs, I can also create (and have tested) bootable clones.
I understand not wanting to erase history; I don't want to either. To use TM to do that is just not my chosen solution so at this point I'll yield to better minds on your problem.
I understand wanting to use a free native app to backup, but sometimes you have to open your wallet to have a workable solution over the long haul. Especially if the native app has long standing issues.