I would look at changing the grips first, coupled with gloves that have a seamless palm area, like the Fox Ranger or Dirt Paw gloves. You can get softer grips than this but I personally use SRAM's locking foam grips. The soak up vibration but the uniformity gives them a predictable rigidity when handling the bike.

I have gloves for: Working on cars; Cold hiking, even colder hiking; summer mountain biking, winter mountain biking, armored downhill MTB gloves; summer commute cycling, winter commute cycling; weight lifting, and miscellaneous woolen gloves for when my hands are cold and I'm doing nothing else.