I find it convenient to be able to comfortably grab the pull-ups bar and do the first pull-ups without jumping, grab the bar and get up 
To get used to it, it is better that the first pull-ups is easy, you know that you are doing real pull-ups from the second onwards but the same thing is true if you jump, in your case you bend your legs after the first pull-ups and you have no problems
In the tool that I have there are two steps to the side to go up and grab the bar, then just keep my legs together I don't touch the ground but the first pull-ups is still "free" because I get up helping myself with the legs at least a little
Given the type of gear you have, Australian pull-ups might be a good idea for training.
For the grip I found the gloves very comfortable and useful, there is no problem of injuring your hands and there is no risk of losing your grip from sweat.
I hope they are useful as ideas

To get used to it, it is better that the first pull-ups is easy, you know that you are doing real pull-ups from the second onwards but the same thing is true if you jump, in your case you bend your legs after the first pull-ups and you have no problems

In the tool that I have there are two steps to the side to go up and grab the bar, then just keep my legs together I don't touch the ground but the first pull-ups is still "free" because I get up helping myself with the legs at least a little

Given the type of gear you have, Australian pull-ups might be a good idea for training.
For the grip I found the gloves very comfortable and useful, there is no problem of injuring your hands and there is no risk of losing your grip from sweat.
I hope they are useful as ideas

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