Kris your guess on whether they are snipe or woodcock is anyone's guess. They depict them walking around in the open, snipe do that. Woodcock's legs are shorter and have a bigger head. I believe they are snipe.

As for me I would fix the cracks either with cyanoacrylate (Krazy glue) or have it glassed.
Fixing it would not hurt the resale since it already had cracks.
Some of these Quality 3's had fabulous wood.