I've made a few arrows, but I've never used real sinew for the task. I've used bamboo to make a few as an experiment. It's fairly easy to straighten with heat, if you're careful with the heat. It's interesting that there's not a lot of differences between medieval arrows and Native American arrows except for the steel points and that the Europeans used linen thread for tying instead of sinew.
Your dowel jig is an interesting way to do the job, you don't have to buy something that way. Back when I was really into making arrows, I bought a dowel cutter to make the shafts that I made. Of course, I also bought bare wood shafts to use, but those got really expensive.