Here is what I mean when I say that you need to have more contact surface between your fingers and thumb.
This first image has a small contact surface.
As you can see the thumb is pinned mostly by the middle finger with the index being in slight contact.
In this second picture the contact surface is greater.
As you can see the middle finger covers a larger proportion of the thumb and the ring finger (hard to see) is also pinning the thumb while the index has the same contact surface as in the first grip.
To do that I have to push my thumb more inward and that requires stretching the ligament. Here is the exercise I use to do it:
Push the thumb as far inward as possible (use the other hand to push it in if needed) and lock it in with the index finger.
Then laterally extend the wrist to stretch the ligament.
You can do holds or slow repetitions trying to increase the range of motion gradually. I like to do this prior to every session, but now it's not necessary anymore.
Also the type of tape you use has an importance.
Here are two types of tapes. The white athletic tape has less traction because its surface is more even. The blue tape is a self adhesive tape which is more rugged and offers more friction which helps prevent fingers from slipping off of the thumb.
The white tape is also less pliable once put on the thumb. If he thumb bends less it is harder to get it deep inward and thus harder to get a good contact surface with the fingers,
The last issue is chalk.. Even with a hook grip, chalk makes an AMAZING difference in how the grip holds up. The chalk works by drying up the skin which makes it less likely that your fingers will slip. This is even more noticeable when you use the "blue" tape.
I have small hands and grip has always been something I needed to work on. I actually studied the best tape to use, the best way to use it and how to optimize the hook grip.