I have had a Tacki-Mac Unified grip sitting around for a while. It's a non-tapered, inch or larger diameter. (I think I recall measuring it at 1.10" one time.) Pretty darn big. In photos it looks very similar to what BGG sold/sells. So anyway I put it on one of my drivers. Not my current one but my previous one, which was always very dependable.
I tried it on the range. Holy crap. I hit two high pushes to the right. WAY right. The clubface was wide-open at impact. I was sort of in shock. So I quickly grabbed my regular driver, which has a built up Tour Velvet midsize grip. Straight down the middle. I've never seen this sort of difference from a club's grip. I mean, it was crazy. Now, the big grip does weigh ~25 grams more, with buildup accounted for. Maybe that was more significant than the size. I dunno. But I thought it was interesting.
If you really fight a hook, that grip might be worth a try.