Hmm, hopefully this makes sense…
I use a very flat surface (a 12x12 stone slab from home depot) and start by gluing everything true and level. So I built the frame of the tray out of olivewood and clamped it square while also weighing it down on the corners to keep it flat on the stone. I use a piece of wax paper under the wood to keep glue off the stone.
Once that’s dry, I apply glue to the edges of the bottom (already carefully test fit) and then press the frame down around it on the stone. I use weights to keep the bottom flat against the stone and again weigh down the wood frame. When I’m done I have a very rigid, very flat, and very flush tray. I apply glue (sparingly)to the inner surface of the tray bottom and around the bottom 1/8" of inner edges of the wood frame and insert the dry second base layer. Weigh the whole thing down and it glues up flat and true.
The key is to not get glue on the inside walls of the finished tray. I sand the tray edges (the olivewood) thoroughly before assembly, and while you can sand the exterior down later if needed, it’s really hard to do so on the interior, so I protect the surface from all the glue I can. I always toy with masking the inside surfaces but in the end i find that being careful is proof enough against glue.
Ultimately, I have about 1/4" of pretty solid glue contact all around the dual-layer base. I’ve not had a tray come apart yet.
Oh, and bonus little technique: I wear nitrile gloves throughout the sanding and finishing process to protect the wood from hand oils and sweat.