I've mentioned here and there how much I like PL400 for gluing up boxes and especially internal baffle parts. The Home Depot is now stocking a line of adhesive/caulks called SIKA. Their polyurethane construction adhesive is far more flexible when set than the PL product with an equally strong bond. They also showed an epoxy in a tube that ha a special nozzle where the mixing takes place so a $2 caulking gun gets it done. Dries to 6000 PSI strong in 20 minutes at 40 degrees. So maybe you have to frame a house while your waiting for the veneer to dry?
Used SIKA Flex 20 years ago on a log home in between the the joints. Big time commercial stuff back then. outstanding quality. Cant say enough good about it. Havn't used it since. nice to see it available in a more public way.