Glad it worked out for you. The key when things go wrong is to not panic and take the time to work out a solution. I try to think about the things that can go wrong and how I'd deal with them while I'm sitting waiting for deer to come by. I bet I have 3 solutions in mind for everything that could go wrong at this point
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I carry a single squirrel step on an OCB strap for just such situations. It's very light and takes very little space in a pocket of my pack.
I climb on a short tether but always have my rappel rig in the pouch on my back. If the stick falls I attach my rappel line just as you did but I also can add the one squirrel step to the tree to allow me to unweight my tether and transfer to the rappel line. Saves me from having to do the hip thrust.