Wanted to mention. If you try splitting the tape, just split a little at a time. In other words, take a razor knife and carefully go around the roll a couple times. The first time around cuts a couple layers, then the second time around it cuts another couple layers (Be very careful with this step, as it takes a good amount of pressure to get through the layers of rubber tape, and you could cut yourself badly.) After going around the roll a couple times you’ll end up with about 4 layers of tape which is 3/8" wide. Then for small grafts just peel off a couple inches or so, pre-stretch it, then apply to your graft.
Part of the reason your graft looks like a dirt dobber’s nest is because it’s harder to stretch 3/4" wide tape. It will stretch, it’s just harder. I was trying to remember how much I stretch mine, and I was thinking about 3X the length of the unstretched. But I looked on the 3M website and they claim it will stretch 700%.
https://www.3m.com/3M/en_US/p/d/b00017540/
I’m pretty sure I’ve never been able to stretch it that far. I still occasionally break pieces when pre-stretching. Much more often when I first started using it.
Also the rubber tape won’t stick to itself very good if it’s wet. But even vinyl tape doesn’t stick very good wet, and vinyl isn’t nearly as nice to work with as the rubber Temflex.
Also, if you have some spare time and are interested, here is an old thread which discusses peach grafting. I didn’t contribute much, because most of my peach propagation is from budding. But there were a lot of good contributions, especially from Scott and Bob. The thread also demonstrates there are many successful ways to graft.