I am thinking about doing something like this too. Let me ask a question....I'm trying to visualize a scenario. I'm asking this out of ignorance....
So, I think you are moving your 30 foot tether up as a you climb the tree and it is connected into your belay loop via friction hitch. Let's say a prussik for simplicity. Now, let's say your stick or hand climber gives way during your ascent and you are hanging from the prussik on your 30 foot tether. How would you add the belay device into the system and shift your weight onto it? I picture myself safely hanging from the prussik, then taking the rope, inserting belay device, putting in the carabiner, clipping into belay loop, adding auto block, but then what? My weight is still on the prussik and I don't know how I would get it over to the belay device...don't you need to have something to stand on remove the prussik from the system?
Sorry, if I"m missing something obvious here.....
So two options and I've done both.
Option 1, firmly pull down on the top of your prusik until you start moving and slide down slowly (so you don't over heat the prusik rope). This is somewhat problematic if the prusik is too tight.
Option 2, My usual approach when changing directions mid climb: Put a prusik or mechanical device above your RCH prusik and put your foot loop on just like you are going to do an ascent. Step down to take your weight off the RCH prusik. PUT YOUR RAPPEL DEVICE ON FIRST!!! then remove the prusik and head down OR maybe just leave the prusik alone and go up, depending on where you are and what you want to do.
I always climb with everything I need to "self rescue" on my person. Won't help if you need something and it's in your bag at the top or laying on the ground at the bottom!
This sort of situation though is partly why I'm looking at the safeguard because it can work in both up and down without having to take off. GriGri or a Guide ATC or a few other devices can do similar.
Also make sure you use some sort of autoblock/3rd hand and learn something called a leg wrap. All this stuff I learned on youtube since my previous experience was rappelling 30 years ago in the army!
Just do yourself a favour and play around on a nice day at or just above ground level so if/when you screw up you don't get hurt!