Welcome to the forum. FWIW my current preferred method for tree climbing is one sticking on a short tether using a stick with double steps and a single step aider.
I do however one-stick back up to my platform on my rappel rope if I have to get out of the tree for some reason during a hunt. In those instances I take my stick down with me as I rappel and just one stick back up on the rappel rope/rig. I say this so that I can attest that it can be done.
I will say though that it is
WAY more difficult for me trying to climb using the one stick on a 25-30ft length of rope for a couple of reasons:
The first is the stability factor. When you're hanging on a short tether (5-6ft) you're pretty much fixed directly below the tie in and it's easy to stay where you want with respect to the tree, even on slightly leaning trees. When hanging at the end of 25-30' of rope you're on the end of a long pendulum and its harder to orient yourself to the tree to attach and set the stick. There's also a delay in the pendulum swing which adds difficulty to the stability corrections you try to apply. Add to that any slight lean of the tree will pull you away from the tree on the downside and it can be difficult to make the early moves. Luckily it gets better as you close the gap to the tie in point. However, you'll likely find you need both hands on the tree/stick to maintain your orientation which means you can't take up the slack in your rope until you've stepped up which negates you're original purpose for climbing on the long rope.
The second issue I find is that there's considerable stretch, even in static rope, when the full length of rope is involved (3% of 30' is approx. 11 inches). This stretch equates to substantial setback (loss of height) with each move when you reweight the rope to move the stick. Although this also gets better as you climb, it annoys me to give up any height I've worked for during the climb and you aren't able to advance your stick as far for each of the early moves. For instance, If I moved the stick 4 times in my initial climb it will generally take me 6 moves to get the same height on the rappel rope.
My personal third issue with your proposed method is practical application of the whole throw ball concept in a hunting situation. Let me again go back to cite some personal experience. The first year I bought a saddle I decided I was going to use SRT rope climbing to access the tree. I practiced all summer in the big maple in the back yard. I got good at hitting my spot with the throwball and was very comfortable with the SRT climb method (I still think it is one of least strenuous climbing methods). Going into season I was all pumped up about my new saddle setup. Once season started I soon discovered there's a big difference between managing the throwball cord in the lawn versus in the woods. The string looped around and caught around every loose twig in the forest essentially making the toss unusable for me. Since I had put all my eggs in that basket I was forced back to my climber that season. The next year I changed climbing systems to something that I practiced successfully in the woods all summer
.
Please don't take this post wrong, I'm not trying to be critical of your idea. Please consider it more as practical advice from a guy who's already done this and is sharing his own personal experiences.