Stacked side by side like that the cabinets will have no problem supporting your lathe. Screw them together on the inside with short self-tapping screws and your stand will be stout.
Rather then stacking all of those 2 x 4's together which, unless you are going to mill the top flat, will be fairly uneven, just use a couple of pieces of 3/4" plywood laminated together. Fasten that to the cabinets and throw your 12ga on top of that. Like you are thinking, build the top a couple of inches wider then the cabinets for a nice overhang and put your switch box on the left side of the cabinet, out of the way. That way you can use the drawer as a drawer.
I built a 2 x 2 steel frame with a piece of 1/2" plywood under my Smithy and it has been good for 22 years... I also built a "rollbar" for the stand that hangs a 48" flourescent light right above the lathe. It is removable if the need arises.
Mark