Firstly, Nancy, calluses are manly....lol kidding
I too find this to be the case to some degree - just can't hold on long enough to really work the back, though I use alternate grip (one hand facing forward, one back) and just try to swap each set. With deadlifts and squats I will still use the same set structure as you with your exercises - 60kg x2, 90kg x2, 120kg x2. Since I'm doing 2 sets of each weight, I swap my grip each time. Makes things feel a bit more even.
Though I would perhaps suggest inward wrist curls (whatever they'd be technically called) with a barbell on a bench for forearm strength. I assume that would assist with grip strength...I honestly have no idea