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Had them down to under 40psi
How far under? I'm guessing 28C GP5000s on 22m rims are going to be about 32mm actual width. My bag of a fag packet calculator points to 2.5bar (35psi) for a 55kg rider as a starting point, +10% at the back and -10% at the front is not a bad place to start for balance, so 38R/32F.
I think GP5000s can be tad harsh because the casing is coarse, but it's not like there's any much better options in 28-584.
Making the wheels less stiff won't help.
What psi are you running? Would suggest dropping 5psi would make more difference than any type of wheel build.