Not to add more complexity to an already complex question, but another issue that underlies the dried versus seasoned sinew debate is how much glue there is in the sinew/glue matrix. It seems that if one were to add a lot more glue relative to sinew, the collagen in the glue might be oxidizing, polymerizing or chemically changing in some other fashion over a longer period of time, and it might absorb and release water at a different rate than the sinew and wood. On the other hand, if the bow maker added just barely enough glue to get the sinew fibers bonded to the wood and to each other, that would create a very different dynamic within the backing over time.
The sinew fibers might also change chemically over time, as there's non-fibrous (non-collagen) tissue within a tendon much like what people find within a deer hide and remove by bucking (soaking in an alkaline solution, usually wood ash) and then acidifying (soaking in an acid solution, usually diluted vinegar). Maybe there's value in letting some of these non-fibrous tissues degrade, leaving just the collagen? Come to think of it, has anyone ever tried treating sinew like a hide before using it to back a bow? As in bucking and then acidifying it so as to remove non-collagen tissues?
As someone who processes a lot of sinew, I've definitely noticed that back tendons that are dried and stored for a couple years are much easier to separate into individual fibers. I have some really long pieces I've been saving that are about 3 years old, and they have a different consistency and feel in the hand than the ones I cleaned and dried just this past fall. Does this mean they'll make a better bow backing? My instinct says yes, just because of how they feel, but I won't know that until I make otherwise identical bows and back one with old sinew and the other with new. I don't have two staves that could yield identical bows at the moment, so I'm not in a good position to do this experiment.