Would it work to use a bag of play sand or something like it as a weight on the face? You could glue up the face (might as well just tip the bottle on - kind of a joke, kind of not) Wrap the face in cling film, lay it spine down and support it so the face remains flat and then lay a bag of sand on it... that would have enough give to match the shape of the face and apply pressure evenly... more weight could be added on top but should distribute evenly across the face due to the nature of the sand. One dry and sanded other specific areas that need more attention can be regales and clamped in a targeted way.
Just an idea I wish I had had when I did our first team captains bat that had slit in 2 across the bat exactly the middle of the toe all the way across for about 3/4 inches up the bat. It was basically 2 flaps at the bottom of the bat...