IMO, you should be fine without sinew backing it for that draw weight and draw length. I would make the handle area pretty small though, to give yourself more working limb.
Just as an example, I made a quick Red Oak bow, 60" long, small stiff handle (The entire handle is 6" long including the fades) and it draws just fine out to 27". I know if I perfected the tiller, I could get 28" safely. If you want to sinew back it, though, go right ahead.
Sean