I did something that might be similar last season. I rotate the bat slightly when I bring it down to drive, so altered my grip after some coaching feedback. As such, I grip the handle off-centre (only way I can think to describe it) with my bottom hand. To ensure that I don’t slip back to a traditional grip, I made the handle an semi-oval but at a 45 degree angle to the spine of the bat. I removed the binding, used kinesiology tape to build up the handle and then rebound it, using glue as has been suggested. Twine has stayed in place absolutely fine.
If you are doing similar, I’ll see if I’ve got some pictures of the process.