I should first point out that I have no experience with high downforce cars so you might want to take what I say with some caution!
The fact that you get next to no movement at the back with 350 lb/in springs is suspicious - it would certainly produce spinning wheels and spinning car if the rear suspension is effectively way over stiff. Obviously heaving up and down to check this should be done with the dampers backed right off. I would expect obvious movement at these spring rates from heaving up and down vigorously on whichever end of the car.
Like I say though, no experience of very high downforce cars like this one but... the impression I always had was that such cars have deliberately limited suspension movement simply because they need to work in a certain range. Wet track = lower speeds = less downforce so are you sure that the car isn't simply 'topped out' on the rebound limit of the suspension. Setting up for the wet may be a bit more than just backing off A/R bar, damping (and spring rate if you've got time) but also other adjustments to ride height and suspension travel stops. You really need someone to post who knows these cars well!
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