DRC is best called Design Regenerate and Rule Check (DRRC), and it can use its own ordering schemes for the regenerate of thermals.
You sound on the right track, but may need to avoid the overlay of planes, - ie make the smaller one 'outside' the larger one, by using a re-entrant path.
You could also try a Zone priority level change ?
I see there is thermal settings by PAD, but they chose 0 as 'use global', when maybe -1 might have been better, in order to allow someone to actually ask for 0 thermal clearance (ie flood-over)
No wait... I just tried a -0.1mm clearance, and it seems to work
ie 0 might be reserved for use global, but negative numbers seem valid.