The technical aspect of your jump doesnt seem too bad, there just isnt a ton of energy added from the take off and swing.
You dont have to move down poles if you dont want to, since you claim you are fine on that pole, but in my opinion if you are looking for drills to get better, you are going to need a softer pole and grip down 3 or so inches, so that you can work on finishing your take off and swing in order to get connected and inverted with the pole. Everything in the vault is a result of what you do before it, so to swing faster and get connected, you will also need to hit the take off harder and with more angle. Until you can do that on a little softer pole you probably wont be able to swing and connect on that pole. BUT when you do hit the take off and swing to the top of the pole, you will probably need at least 2 or 3 bigger poles than that one. Its your choice. Here are some drills you are craving
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Ring workouts
ring bubkas
bar workouts (pull ups, dips, etc)
bar bubkas
plyos like standing triple jumps or 1 legged hops to improve take off.
This might be a good opportunity to check out the training forum for literally countless other ideas on how to improve your take off and swing.