To actually answer your training question, regardless of unknown aspects of your vault that may be causing your hand to slip, and assuming you already know about tape/chalk/sticky spray:
-Gymnastics (highbar, rings, rope) drills practicing your swing to inversion will effectively strengthen your hands while reinforcing technique and muscle memory. When I was a younger I made a makeshift highbar by fastening a metal pipe in between the trusses in my garage. Swing ups and straight leg raises are better than pullups, but any time you spend hanging on a bar/rings/rope will help your grip strength.
-Rock climbing/bouldering. Not sure if there are other climber/vaulters out there, but my vaulting buddy and I spend most of our spare time not vaulting, and all of the off-season, climbing rocks. Bouldering especially trains core muscles(front and back), hand strength, power-endurance, explosive movements, not to mention the mental aspects of commitment, height, danger, and memorizing complex series of difficult movements (and learning how to fall!). As a masters vaulter, the best thing about bouldering is that it allows my sore knees/shins/back to recover between vaulting sessions while still building strength...not to mention it is the most fun thing I have ever found next to pole vaulting! Another benefit of climbing vs. weight training is that it only builds lean muscle, you don't bulk up like you would if you spent too much time in the weight room...
I am not sure what part of New York you live in, but there is excellent bouldering all over the Empire State and Pennsylvania: at Niagara Glen (in Canada near the falls),at Nine Corner Lake, McKensie Pond, Poke-o-Moonshine (all in the Adirondacks) and the awesome Shawangunks near New Paltz. There's probably a lot more places...check out this link for some info that might help you find it near your home:
http://www.rockclimbing.com/cgi-bin/rou ... 2FNew+YorkClimbing indoors in a gym is great for strength building as well, but lacks the beauty, complexity, and commitment of climbing on real rock. Roped climbing is also good but is usually not quite as explosive and concentrated as bouldering, better for endurance training.
There are tons of other grip strength exercises you could do, but these are the two I would fully recommend. In my opinion, the best types of training are those that are fun enough to ensure long-term commitment! Give it a try and let me know how it works out for you.