Can't see your second batch of pics so that didn't help me to evaluate what you've got in store.
I don't have good access to either rawhide or hardwood backings (or the power tools to help me apply it to a back), and I don't like pounding and shredding sinew.
But I regularly back decrowned staves with plant fibers or occasionally with linen (flax) canvas. Works like a charm for me.
Few people use it, probably because they use the above alternatives.
Of plant fiber backings, I prefer sisal for backing. When I take a single fiber of 15 cm, I can stretch it till it breaks around 15.4 cm. That means it stretches e-nearly 3%, which is plenty for a normal bow.
It's not overly strong like flax or hemp but more like bamboo, so it doesn't overpower the belly. Works best on wide bows, so a pyramid design would be pretty good. I get the sisal from hay bale twine and apply it like sinew. It's coarser than sinew and more stubborn, so the hide glue needs to be less runny / tackier than for sinew (or flax). If you add 15 g of shredded sisal per limb in bundles of 20-25 cm long you get a layer of c. 1.5 -2 mm thick in the center, which is enough for a 50# bow.
To patch lifting splinters, I prefer raw flax, as it is extremely strong and very soft. Occasionally, I back a bow with flax, but only a very thin layer, otherwise it forces the entire underlying wood into compression. In my experience, flax has the tendency to lift with lower grade hide glue, especially if not wrapped tightly with bicycle inner tire after application. Makes me nervous when it does. Here in Belgium, flax is sold in bundles of 300 g (resembling long blond hair
in a plastic tray) for 5€ a bundle in any DIY store.
As for your boards: I recently made a board bow from norway spruce (about the least wanted bow wood in the world). Grain didn't run off as much though. same width as your intended bow (4.5 cm). Pulls 35# at 28". Seeing your white oak boards and the low draw weight, I would dare to just go for it, bare backed... But I couldn't see the detailed pics so I might change my mind.
Maybe you could turn the grain runoff to your advantage. Mentally peel off the rings where the run-off is, and see what you get. You may end up with a nice trapezoidal cross-section, which would fit white oak perfectly. You could even cut the pyramid diagonally (leave one side of the board as its current edge, and vice versa on the other end, so as to have less grain runoff. But of course, the lateral grain runoff is more an indicator of harder to see grain violation on the back.
Lots of 'if ... then's. Good luck with it.
Joachim
