re: Should I change the way I grip my pistol?

I presume it's your right (strong hand) thumb that's causing the problem.

Neither thumb needs to touch the gun. I'm no expert, nor am I a Ninja class shooter. But FWIW both of my thumbs "float" alongside the slide, and both point forward.

As was mentioned, locking the right (strong hand) thumb onto the top of the left thumb will//should also help solve the problem. Massad Ayoob recommends this (he calls it the "crush grip").

Another option, if you are unable to get your thumbs well away from the slide, is to change to a "high thumb" grip with your right (strong) hand. Tom Givens recommends this (but he doesn't insist on it) to avoid the problem you're describing and to avoid accidentally flipping a 1911 safety "up." But you still need your left (support) hand "cammed" downward, which results in that thumb pointing forward, to take advantage of the tendon/muscle lock that causes the gun to come back down after the recoil impulse.

FWIW I spent two days with Jerry Miculek a few years ago getting one-on-one training. Jerry never suggested having me do anything different with my thumbs (both forward, neither one touching the gun).

I have also taken a three day pistol class with Clint Smith (Thunder Ranch), and two-day classes at a number of other schools. No one has ever suggested that I needed to have my thumbs touching anything (the gun or the other thumb). But none of these instructors has ever said that you have to "float" your thumbs if what you're doing works.

I'm sure the foregoing is confusing. It's easier to show this stuff than to describe it. This is one of those elements that you need to experiment with until you have something that works 100% of the time -- then get enough repetitions to burn it into your muscle memory (neural pathways).

Just my $.02 worth.