3M™ VHB™ Tape 5952: An industrial strength double-sided tape. $90 for one 36-yard roll (1" wide), which should be enough to complete five panels.
HiPURformer™ hot melt glue: Apparently the only product of its kind, this is a cordless glue gun and cartridge system. Polyurethane glue is a very durable adhesive (most common brand name is Gorilla Glue). The MP75 formulation supports multiple materials including metal (as opposed to being specifically for wood like the other formulations) and sets up in 75 seconds after application. Base kit is $100; each $11 cartridge produces about 71 linear feet of bead, which should do about 1 1/2 panels, so 3 tubes should be enough for 4 panels. Advantages of this system are that it is flexible and potentially useful on other woodworking projects, and also less expensive once the gun kit is purchased; disadvantages are that glue is messier to apply than tape, and this particular kind of glue has only a 6 month shelf life.