In terms of cost:
What you already have for stick climbing=Zero
(1) mechanical=$$$
(1) hand ascender=$$$$$
You've already said your climbing with sticks and rappelling down with the only time you'd ever climb the rope being those one-off situations. If you left everything up in the tree and rappelled down for whatever reason, you'd still have everything you need to climb up attached to your saddle, ie: linemans belt.
With that linemans belt, you have:
- rope which can be tied into a foot loop and connected to the rope with a prusik hitch
- a prusik (or mechanical) which serves as your rope attachment
- a carabiner which connects your bridge to the rope attachment
That's all you need. It wouldn't be the fastest but it is functional and costs you nothing. Only if you intend to climb SRT do you really need to go down the rabbit hole.
Case in point since I do climb SRT 99% of the time. I did a evening sit and intended to come back to the same tree in the morning. Instead of removing everything only to set back up a few hours later, I left everything in the tree except my bow. Once on the ground, I realized that by leaving everything in the tree, I also left my hand ascender and foot loop.
Since I always carry a spare tether on my saddle, I simply rigged up what I previously mentioned and climbed the rope nearly as fast, easy and silently as I would my hand ascender.
Lastly and only because everyone loves my drawings, here's how you'd attach a linemans belt to the rope to climb. Simply swap the (blue) prusik foot loop shown for your linemans belt rope. If you use a mechanical instead of a prusik on your linemans belt, simply swap the mechanical for the upper (blue) prusik shown.
