process of elimination...
sounds like not a tire issue... can't remember what width you run front and rear... I'm running a square setup, so obviously I get more relative front traction than most setups... assuming yours are not overly staggered and that your front tires were in as good condition as the rears... if so, we can rule out the tires themselves... that is, unless you have something weird going on with tire pressures
didn't occur during braking, so those are out
we can rule out the rear diff
so that leaves setup or driver
on driver... this is a low speed (mechanical grip) corner... you're an experienced driver, so I'm sure you're all over this, but have you tried different ways of entering and exiting that corner? wet tracks = slower in, later apex, more gradual acceleration... and of course when you accelerate you will be transferring weight off the fronts and onto the rears, which brings me to setup
on setup... thing #1 is to disconnect the sway bars in *hard* rain... an old racer trick someone shared with me that tends to alleviate a lot of the twitchiness in the chassis on a wet track...
also, can't remember which coilovers you have... how much adjustability do you have? what are the spring rates you are running front and rear? if you are having this issue of understeer in dry weather as well (you said it was amplified in rain), especially on an uphill exit (where the front *should* have LOADS of traction), then you might think about going up 2K in rear spring rate and before then even try adding some compression (bound) stiffness the rear dampers... and/or maybe take out a few clicks of compression stiffness in front... I always have to remind myself, one change at a time
finally, post up your caster/camber/toe settings on front and rear, if you like and we can comment on those and how they might be playing in... only if that's helpful
others more knowledgeable than me can expand on what might be going on with your setup... also, read these
Effect of Suspension Changes - trackHQ.com - Track Day HPDE W2W Club Racing Time Attack Motorsport Forum
Front anti-roll bar stiffness and understeer? - Corner-Carvers Forums
And final question... please tell us what your tire temps are if you are collecting those (inner, middle, outer) and if there are any obvious wear patterns on the front tires