well, that advice was made when I thought the sinew was limited to a repair. now that i have read back to the first post and see the whole bow has a sinew back (sorry about the misunderstanding), I guess your options might be limited to applying more sinew, or at least some other fiber with the hide glue?, or removing the sinew to make a repair in the hackberry.
where there is a will there is a way.
actually, plant fiber can be much stronger, it does not stretch as much, but you are looking to stiffen, so plant would be a good choice. I would hesitate to use a different glue on the sinew if you might want to keep your options open for reuse of it.