Hi Tom,
I have built many of these kits. It’s not so much the adhesive as it is prep work. Are you sealing the wood with sanding sealer? If it is not sealed, it will not stay glued. You can buy a quart at any big box store for less than ten dollars. Small pieces I use acc. Larger pieces I use a two part epoxy and lots of clamps. The longer the set time for the epoxy, the stronger the bond. Any boxes mounted to the underside are glued and then I run small wood screws into the boxes from the inside. These are flat heads with holes counter bored. If you choose to use acc, use the thicker types and be patient with the set up. JB weld is another choice of epoxy. Also when using sanding sealer, do many coats with plenty of sanding in between. You shouldn’t be able to feel the grain.
Tom Mapes