The artificial sinew actually can work very well. First, cut a piece about 10" long. Then begin splitting it into smaller strands until you have a piece not much wider than a line drawn with a pencil. It's pretty easy because artificial sinew is comprised of several of these smaller strands.
Start your wrap, making sure to wrap the sinew over top of itself once or twice, but do NOT do a lot of layers! A lump makes an uncomfortable day of shooting! Pull the thread as tight as you can get it, wrapping carefully so that each wrap lays tight against the next. When you get to the last of it, use your fingernail to smoosh it into the shaft as you rotate the arrow. The wax will hold all in place...for just a little while.
That little while is just long enough to reach over to pick up a small bottle of superglue. Dribble a little on the artificial sinew wrap and smooth it with your finger, wiping it all around the sinew. The superglue eats thru the wax and bonds the material to the shaft. Careful you do not use so much glue that it wicks up onto the feather. That turns it from a flexible feather to a blade slicing across the back of your bow grip hand.
I knocked out a couple hundred of these for a German Documentary film crew several years back.