I've seen a flannel sheet hanging in my friend's garage catch field tips neat as can be without tearing.  He hasn't tried it with broad heads.  Medieval Japanese horsemen would wear a piece of fabric fastened to the back of their armor and it would fill up like a sail when they rode.  It would deflect arrows shot at them while they rode away.  Based on that, a simple fabric backdrop might work just as well on stone points.  It must hang loose from the top corners, not be stretched tight, and not fastened at the bottom.  I don't know if your points would break against the fabric or not.  You would need a soft floor for them to land on, after bouncing out of the sheet, to keep your points from breaking.  A piece of tape or a silhouette inked onto the sheet might work for a target.