First of all, it would make little sense to have the existing outlet circuit
daisy chained from one bathroom to another unless it was in fact protected
by a GFCI device upstream of these outlets. This was done commonly in the
80's. If you want to run new circuits to upgrade the bathroom, the easiest
thing to do would be to run one 20 amp circuit and just use it for the
outlets in the renovated bath. You can use the existing lighting circuit for
any new lights and fans, etc. provided you're not adding any electric heat
or Jacuzzi, and things of that nature. You cannot disconnect either of the
existing circuits at the panel, as they are feeding things other that the
renovated bathroom, so you have to locate junction boxes in some accessible
place to splice those circuits through, to wherever they're going.

I currently have one 15A circuit doing the bath outlets (for both
baths) and another 15A circuit doing lights for that bathroom, a
closet, and another bathroom. Tell me if this sounds reasonable:

1) leave the existing 15A circuit that currently powers the existing
lights, etc. and remove bathroom B and closet from that circuit
2) leave the existing 15A circuit that currently powers the outlets,
and in the attic, cut the line to remove the outlets from the circuit
and splice/branch out to do the second bathroom's lights (and maybe a
closet light?)
3) run new 20A circuit to 2 bathroom outlets in bath A, and then over
to 1 bath outlet in bath B, with GFI on the 1st outlet in the run

Does this sound logical?