Back in the day of tying quilts, I think I would just pluck a Crewel needle out of the big paper assortment of many needles. Personally, I like a long needle but I'm pretty bad at handwork. One of my hand applique friends would always cluck at the "huge" needles I used for hand sewing on my binding. She used these tiny little things I couldn't even see back when my vision was considered normal!
Basically I'm saying the same thing as Tartan, but I look at it as finding the right eye for the thread, and figure the diameter will just have to go along for the ride of the thread. I also use a long thread technique, you don't want to have to thread the needle for every tie, but I give myself a bit more thread to work with, just a gentle tug to pull up some extra between the ties, but I tie and cut about every 3 ties instead of going across the frame -- mostly because I don't have a frame.