One thing that I think helps is just hanging. Gets you used to carrying your bodyweight in a way that assisted doesn't. What you're doing will still help with full range of motion, but maybe at the end just hang as long as you can. At some point you can also add this at the top (e.g. hop up to bar to chin and hold as long as possible)
Oh, that's great, I think you've got to be almost there then!
Something else you can start adding is holding at the top then lowering down with as much control as possible, and pausing every inch or so. You can also work on shifting weight from one arm to the other between each pause (e.g. lower an inch with as much weight as you can on the left then pause for a second to shift as much as you can to the right and lower another inch).