Maybe not that tricky.
I don't know the layout of the area other than aerial photos, but it may be possible to lay a seige on the mosque with small arms. Pull the tanks and artillery out of there, and the helicopters. Keep anyone from entering or leaving. At some point, they'll either give up, or blow themselves up when there is no American weapon in range that could have done it.
They'll still blame us, but it won't be as easy.