This idea is based on the premise proposed by me in the first Comment, dated 1/1/2009, that the fundamentalists of both sides are the source and momentum of the problem and that reasonable people can solve this problem but unreasonable people are the barrier.

If indeed the unbendable, uncompromising fundamentalists of both sides are the source and momentum of the problem, and if we grant that reasonable people can solve this problem in the absence of the uncompromising elements among their ranks, then one solution would be for the reasonable powers within each side to come together and agree to identify and simultaneously arrest and deal with the fundamentalists among their own numbers.

The devil is in the details, of course, but the beauty of the approach is in the fact that each party can more easily identify its own radical elements. In short, instead of trying to find the other side's trouble-makers, each side agrees to find and contain its own.