"I often have the impression that sinew backings without a horn belly is like a monkey with a golden ring: you'll never stretch the sinew on such a bow for more than 2, max 3%. And if you would, no belly could stand that compression. Plant fiber backings can stretch up to 2% if I recall well, so I don't have the impression that one ever really needs the sinew's full capacity, unless on sinew-wood-horn composites."
I admit to having very little experience with sinew on bows, but I will agree that the absolute best use of it is likely on Asiatic composites. On the other hand, I have the impression that wood bellies EASILY resist the compression induced by sinew backings. Sinew is a very "soft" backing. It stretches a lot, and quite easily. I always understood that a sinew backed bow stored energy IN THE SINEW, as it stretches, and the very fact that it does stretch means the belly is forced to compress less. My few experiments with cable backed bows bears this out to me.
The part about the sinew not experiencing ENOUGH stretch is totally valid. This why short, reflexed bows, or those allowed to dry into reflex are the most appropriate designs. Those designs make the sinew work. A big flatbow absolutely will under - stretch the sinew.
On the other hand, bamboo and hickory backings "overpower" some woods specifically because they are so stretch resistant. Plant fibers WILL stretch a little, but they resist it, Baker says they "stack" before they break, and they don't stretch far.
"Bamboo does stretch, just like any other bundle of cellulose microfibrils, it's just very strong in tension, especially given its rather medium density."
The very outer surface of most bamboo species is MUCH heavier than even the more common tropical hardwoods, though. I had some tropical bamboo from India once over 1.30 SG.
"I find woven backings much harder to apply than bundles of fibers, but if you have a good technique for doing so, is there a post where you describe it?"
Nothing to it. I rough tiller a bow (mostly done this with board bows, of course) ad use a big C- clamp to hold the handle down to a 2x4. The key is the clamp goes under the board and clamps the sides of the handle. I place blocks under the tips to push the bow into reflex, as much as I think it will take. Then thin some TB III with just a splash of water, paint it on the limbs as a sizing coat. Let it partly dry. I cut a linen strip as wide as the bow's widest point.Then slap down a layer of glue from the bottle, smooth it evenly, and lay the strip of cloth down end to end. Finally, I use the thinned glue to moisten the fabric so it will relax and pat it down against the limb, smoothing and lubricating the fabric as I settle it down with a finger or paintbrush. It has never lifted on me while drying, except once on a crowned back. When dry, I trim the sides with a knife and file the edges smooth to the limb edges.