If the twine will be for safety against breakage and you are building with a board, my thoughts are the proposed width profile/crossection combined with the proposed recurve tips will result in a lower poundage bow once tillered out.
If you wish to optimize the board for the best bow possible, and are open to suggestions, could you post how long/wide't (-_)hick your board is and how many pounds pull and draw length you are looking for?
maybe mention something about the previous bows you have built?
The board I’ll start with will probably end up being roughly 2.5 inches by 1 inch (might shoot for 1.5 to be safe), and about 66” long (before I recurve the ends). As for poundage, I’m looking to make it 35-40 lbs at 24”, although I don’t have a reliable set up to test that quite yet.
If you are talking board bows, they I have to recommend my friend Weylin Olive's YouTube series on building a board bow. He breaks it down DEEPLY and still keeps it moving along and interesting. The very first one of the series is about how to choose the board. If you follow his instructions, then you have eliminated 90% of all the problems you could run across while making the bow....including eliminating the need to back the bow. A well-chosen board needs no backing, ever.
At the low draw weight you are looking for backing is definitely not necessary because draw weights like that are not a great strain on the wood.
"I put one on my first bow I made with wood glue, and it seems to be the only thing holding it together". How do you know that is what is holding it together? Has it had a catastrophic hinge and failed? That is the only way I know of that you can test whether a backing is actually holding a bow together.
I want to put a challenge to you. Send me that bow, I will remove that backing and prove to you that the bow is still holding together. As an admin on a Facebook page dedicated to board bow building with 26,000 members, I have seen dozens and dozens of these bows backed with this material....and they fail just as often, if not more often, then unbacked bows. ALWAYS, with EVERY bow, no matter the hundreds of choices you will make in the process, the first step will forever be your choosing the piece of wood. Pick the right grain, only the right grain will do.
If you do not choose wisely, every subsequent choice is only mitigating the degree of failure. I hope this is not coming off as harsh, but I have to rush to get this done and get my butt out the door. I don't mean to discourage, in fact, just the opposite because I really want to see this bow you are describing. It sounds like it would be elegant, graceful even. And if you play with bows for long, you will discover that good shooting bows are always elegant!