On a second thought it is probably possible to combine OnionBalance with Whonix. I’ve managed to wrap my head around the upstream OnionBalance documentation.
Please see, try, test, leave feedback, edit if needed:
https://www.whonix.org/wiki/Onion_Services#OnionBalance
It is still untested at time of writing. Should that change, the notice will be removed from the wiki and a new post will be made here.