Well you have been having some grip problems while doing forearms twice a week if I am getting this. Yet you blame it on pullups as if there is no carryover.
I think someone told you that forearm work alone doesn't lead to a great grip. VERY TRUE. But don't reverse it and think that a lot of forearm training doesn't affect your grip either positively or negatively depending on whether you do it appropriately. It would be EASY for everyone to have popeye forearms if they weren't simultaneously trying to bring their deads up to superhuman levels. Likewise it would be much easier to be a grip master if you weren't worried about pulling....
Yeah, holds, pinch grip training with plates, thick bar training, and of course utilizing a double pronated grip all the time is supportive grip training.