If this is a new remodel, and walls are going to be open, you might as
well run new 20A. Don't bother trying to use the old 15A wire as a
drag line, just cap it off in the panel. I believe code now calls for
20A in a bathroom. If you are going to have a fan/light/heat combo
unit, that alone needs its own circuit
It would be different if you had to tear walls open if you have to run
a new line, but since you have access to run cables, might as well do
it.
I would also like to add if you are putting a fan/light combo inside
the shower/tub area, it must be GFI protected. You can just get the
feed off of the GFI outlet to accomplish this.

The bathroom walls are definitely out - I stare at insulation and
studs every night when I get home - ugh.

I may be missing something - if I am please forgive me. You said the
fan/light combo must be on a dedicated circuit, but then you said that
I could catch the GFI for the fan/light off the outlet run, implying
that now it's on the same circuit as the outlets.

And just wanted to confirm - I shouldn't mess with trying to fish the
15A cable out and then fish a 20A wire down via the attic? Did you
think that I should run across the crawl space and then up the HVAC
chase two floors?