There is no exit strategy as far as I can see. Unless we're willing to follow through on our threats we need to back off.
Do we want another Libya or Iraq? I guess some folks do, but the vast majority of the American people don't. And if we're doing this for some sort of humanitarian reasons then we should get the support of the US public before going on another foreign bombing spree.
I think if Reagan were around today....around six months ago....quietly and not saying anything to anyone in advance....he would have fired off a dozen cruise missiles on Syria. The warning would be that you need to do a regime change or something, but he’d make sure that warning avoided taking massive steps later.