The diagnosis sounds right to me but...
Twenty some minutes of backwash (and I'm assuming that is including the rinse time) is about right for a residential sized AN filter.
If you have a water softener it and the filter should be programmed to allow the softener to go into a regeneration until a couple hours after the filter does its thing.
You'd have to have someone look into the septic tank (literally) to see if the water/scum level is correct. Also, there could be something broken etc. on the outlet of the septic tank that is reducing the outlet flow and causing too much water in the tank.
I think 10-12 minutes of backwash and then like 10 minutes of pause before going into a 5 minute rinse might help. And to prevent a softener from regenerating for an hour or two after the end of the filter backwashing would cure the problem. Maybe the overflow is only when both do their thing on the same night.