DannyBows, I wrapped the nock end with several layers of yarn, glueing each layer as I went, until it was built up enough to grip easily.
Dave, Dannybows answered your question. You don't need a rest and can use a much shorter arrow.
Now, for the next one. I have been thinking of using a bamboo cane like an atlatl to throw an arrow/dart. The difference being to again use a short arrow/dart of say 12" with the string grove in the point. The launcher could be a shorter one of 3 feet for one handed launching, or maybe 6-9 feet for a two handed launch. Probably it would require a fork at the end of it so that it launches cleanly.
Last night I tied a 6" loop of artifical sinew to a 3 foot piece of bamboo that was about 5/8th " in diameter. Putting the 12" arrow/dart onto the loop, I launched it toward a target butt, then I did it about 6 more times. On a couple of the launches the a/d entangled in the loop and didn't release, but I was supprised at the speed of the a/d as it flew to the target. Now I'm thinking of a forked launcher and the next round.