The backwinding is different on one tack than the other. I think
that's a function of the weather cloth on the genoa effecting the
leach shape differently when it's to windward than when it's to
leeward. Another strike against roller furling sails.

That's one possibility but it could be mast/rig tune also. If you can
get a good sail maker out on the boat, they can show you a lot. You
will also get a sales/sails pitch of course but that is to be expected
and may even be the right answer. There are basically two possible
reasons for excessive backwinding (a little when close hauled is OK):
Either the mainsail shape is too full or the jib draft is too far aft,
possibly even hooked. A main that is too full can usually be recut if
it is not too far gone and good use of sail controls such as
cunningham, halyard tension and outhaul can also help. If you have a
bendy mast, a little mast bend will flatten the sail but you need to
add more cunningham/halyard tension to get the draft back forward. If
the genoa is the primary problem the solution is different. Make sure
you do not have excessive headstay sag, that adds fullness and moves
the draft aft. Make sure the cars are not too far forward. If the
sail is basically in good condition and all else fails, have your
sailmaker recut with some extra leach hollow.