Mounting camera into a camera trap box

If you only have a limited set of tools, you could put a quick release on the base of the box with a slide plate, and use the slide plate to adjust the camera + lens.  You would attach the quick release with screws through the bottom of the box. Here two from ebay:

• cheap slide plate (Hong Kong seller)
• Giottos MH621 (US seller)

If you make the back of your box removable, you can slide the camera out with it on the plate, and then remove the plate to change batteries/memory card.

If you have a woodworking shop with a router, I imagine you could do:

• Make two parallel cuts in the bottom of your box.
• Then put a 1/2" piece of plywood under the camera.
• Drill a 1/4" hole for the tripod socket screw (I would drill a 1/2" or 3/4" hole about 1/4" down in the wood, so that the 1/2" screw is flush with the bottom of the wood).
• Drill holes in your wood to match the parallel cuts in the base of the box.
• Add 2 1" or longer screws with wingnuts that fit through your plywood, and the bottom of the box.
• Add a wooden stop peg or piece of wood in front of the camera to prevent it from twisting.
• Have removable back.  Or have the side removable, and just have the back long enough that you can slide the camera out and then remove it.

A simpler alternative might be use the router to make a 1/4" cut in the base, and then use an appropriate sized 1/4-20" screw to anchor the camera, and undo the screw to adjust position or remove the camera. I suspect it may be hard to get it tight enough to lock the camera in place with only one screw.