Trey Ceiling with LED Light Channel

Adding a trey ceiling with LED light channel in our dining room. Doing the trey is standard as have done in other rooms, but want a channel to run LED strip lighting. Having trouble with the vertical leg light channel. Should I use plywood on the bottom of the trey and also on the vertical leg to create the light channel and then attach the drywall? Any suggestions appreciated. Need light channel to be about 3" wide and the leg about 3" high with a 2" deep channel. Trey will be 8" high and 18" wide including light channel.