Are they SURE that Seminole bow was made of mahogany? Everything I know about that wood (which is only a little) tells me that it is very brittle, stiff, but not at all elastic. That's odd.
And that is exactly what I would expect, from the wood.
I have patched a back with linen before and had it last years, by glueing on individual raw linen strands like sinew backing, fading them out, and then wrapping the whole thing to hide it. But it is ugly, not at all historically accurate, and sketchy.
Toss the board. Good luck next time.