Yeah trying to get sinew from the local meat processor is like asking them for $100. They don't save it, and the only way they will save it is if you beg them to and maybe have to even offer them a little money. The best way to get sinew is to cut it out yourself, if you hear of someone you know getting a deer, give them a call right away and ask them to save all 4 legs for you, to cut off all the meet they want, be sure they understand you only want the bones with everything in tact except the meet. Then you take them home and very carefully, pull off the skin (the fresher they are the easier this is), and flex the bare bones at the joints so as to watch where the tendons are and how they run. This way, if you do it right you can get some 10"-20" leg sinew out of an adult deer (when they dry they shrink somewhat and harden, but should still be 10-16" long). With a little practice and patience you can process the sinew from an adult deer and get enough for a layer of bow backing. If you don't know anybody that gets a deer, ask the meet processors the same thing, BUT AGAIN--YOU'LL HAVE TO TELL THEM LIKE 10 TIMES THAT YOU ONLY WANT BONE WITH SINEW INTACT, NOT MEAT!!! And you may have to offer the guy 20 bucks or something as an incentive for the extra work of saving you the legs. Another thing, most people that butcher deer hang them by the very tendons that we seek, so ask them to not sever the tendon in the hanging process.
