There are plenty of options. Gluing the 2x6s together at the edges is one way to go. You can use dowels/pegs to join them at the edges, or use pocket joinery, in conjunction with the glue. Probably the simplest thing would be to strap the 2x6s together from the underside with pieces of 1x3 strapping used for hanging drywall on ceilings.
I agree that you should have some kind of bracing on the back. Maybe not a full "X," but just some corner bracing cut from 2x4s.
None of these techniques will stop warping. Glueing, screwing or doweling will never stop a board from warping. Strapping won't really help either. All wood moves. You can't stop it. You can however minimize the problems. First is to understand wood movement. It will move accross grain more than with grain. In other words the 6" will shrink and expand more than the 8'. In a tabletop you glue up the panel and use a breadboard edge to hide the movement. It is only glued in the very middle of the breadboard edge and it is pinned with wood dowels or pegs on the ends. Another way to minimize the effect is to look at how it is milled. Construction grade lumber is plain sawn. There is also rift sawn but the method of sawing with the least movement is quartersawn. It's also the most expensive wood because of the waste.
Joining the boards to make a single width.
With construction grade lumber more than likely you will see the grain curve around the end. It will warp towards the center of the tree. Join the boards with all the rings in the same direction and it warps in a circle. Alternate them and it warps like a wave.
That wood warps is why you never see a paneled door with the panel glued to the stiles and rails. They float in the grove. Glued together it could split the door or you'd see cracks where the boards were glued together. It's also why craftsmen use plywood with a solid wood edging. People talk about plywood cabinets, etc. being lower quality but in reality are the better made.
One way to minimize warp is to seal all six sides in polyurethane. It is a solid coating and minimizes moisture changes in wood. Won't eliminate them but slows it down.