Should I glue to luan backer?

Making a desk for my husband out of ambrosia maple and walnut. It’s a lot of pieces to be glued up and after fixing the warps twist and bows from a SC summer, the boards are about 5/8” with the planing left to do one the MC gets to an appropriate point. My questions are this… Should I attach them to a 1/4” backer? If so, how.. glue or nails? Would glue allow for natural expansion in the future? Would I edge glue them first or edge and face glue at the same time? I had someone plane them and join them recently but after letting them dry out more, they may have changes shape again. Any advise on how to do this with hand tools and a table saw would be appreciated. It cost me $50 for a local woodworker to do it… I’d rather use that toward a planer/joiner in the future. Here is a drawing of it will look like, bow front top is 84” x 24” at corners and 36” in center. Other side is scaled appropriately.

.