Yes, you will be shredding sinew for days. The thinner you seperate it, the nicer it'll lay for you. Also, try applying smaller bundles of sinew and make sure they are flat like ribbons when you lay them down. I seperate the sinew until it begins breaking lengthwise, then back off a little, so it's pretty small in diameter.
When it dries, it will be rough on the surface, it's ok to scrape it and sand it to even out the surface. To help with a more even surface, you can also brush or wipe on a little hide glue after your last sinew layer, and also do it again after it's all dry, then scrape and sand again. You can make it really smooth if you like. I like a bit of a textured look... or cover them with snakeskin or fishskin, etc.
You can keep your hide glue mixture in the freezer until the sinew dries, then thaw it, and reheat it quickly for the leveling of the surface.