Putting it all on at once is like applying a thick coat of paint.....it dries unevenly. One of the tricky parts about sinew is getting it to dry and cure without self destructing. It will crack, warp, pull away from the wood, and may even crack the wood. Damp sinew will behave itself, but you don't want damp sinew on the back of a bow.
If you look at sinewed bows from history, I think you'll find that the thicker the sinew, the shorter the bow.....or at least the shorter the working area. Longer bows do not benefit much from thick layers of sinew.
Personally, I prefer to apply thin layers of sinew. One, maybe two applications. I usually wait a week between layers.