I would design the circuit in a way that the voltage regulator has the same GND as the reference circuit. The GND for the heating is on a star point before the 15V regulator. So any drop in the ground should be regulated by the 15V regulator.
I would like to use three 6V 4,5Ah batteries, so there should be enough power even for days. I think an extra cell is a big deal in sealed-lead-acid. It is heavy and big.
My problem with separated batteries is the charge circuit. I have to build two isolated charge circuits as well if I would insulated all the things.
I think 35°C on a summer day isn't a big problem in germany

Thank you very much for these tips. I think I will build up the heater with a 15V regulator for the reference and do some measurements on the 15V rail during extreme changes in heating power. After this, I could decide which way I should go.