So you had used a power lam, but the handle popped off anyway, is that what I am getting? Hmmm...
I have made a bunch out of boofloo and never had that problem. They were usually tri-lams in a R/D, and the bow didn't bend MUCH right off the handle/fades, but did bend there....
Did the fibers pull apart crosswise, or do you mean that it tore some up, like lifted them out, so they separated lengthwise?
On the boofloo, the handle came off, but the backing and power-lam did not fail, right? If so, try gluing another thin (1/16" to 1/8") power lam of something pretty stiff under the handle, lke another piece of hickory, osage, ipe, etc..
I don't flex lam bows until I am pretty happy with the shape of the fade-outs at the handle. If you were tillering with a squared handle block on, that may be it...