I'm sorry to hear of your mishap and hoping for a full and speedy recovery. Thanks for sharing, this particular failure mode is probably the one that concerns me the most one-sticking. I hope othere can use this to be aware of the potential downsides.
I try to keep my fingers out from between the rope and the tree as much as possible. I typically advance the rope primarily with my right hand holding the outer edge of the link making my girth hitch and then kind of push the rope up the backside of the tree using the top edge of my fingers/knuckles of my left hand. I'd like to say I never get a finger in the precarious position but sometimes it just happens.
I'm curious, were you standing on the top step when the stick kicked out or on the bottom step? Personally my most uncomfortable move is stepping to that top step. I only do that on my final move, after I've advanced my tether and set my platform. The stick is way less stable once weighted above the tie in, especially with your already noted separation between tie off points. For all my other advances I always just stand on the stick bottom step.
Again, glad you're not too seriously injured (although I can attest broken fingers on the right hand suck for so many reasons
) and wishing you a speedy recovery.