a good place to get cattle sinew, is find a feedlot in the area, and ask them if you can go over to their dead pile, and cut the tendons off, they usually die from pneumonia, colic, "the spins" or a lead pill,not anything that is contagious to human contact.
chat to the cowboys at the feedlot- make friends with them, trade them some gear- they are worse gear freaks than trad archers, offer them a new hat or sumpin' for"x" amount of sinew.