The only auto-rest at 0600 is if you are going into a golden X day or a vacation day. A REG day off does not fit either one of those definitions.

As an alternative strategy, look at working a RES spillover rotation into REG days off. That pays double pay on the REG days, like a GS. RES Spillover rotations are all proffers and that step of coverage is before GS, so even if you've already had one more more GS in the RES month you can grab more premium pay before anyone wanting a GS gets a shot at it. Pay on the LC day(s) pays towards RES guarantee, so make sure to pick a trip that places most of the block/credit in the REG month.

You can only do a RES spillover rotation from LC days to REG days off. You cannot do it from X days to REG days off. The rotation must report on a LC day.