is weldwood contact adhesive strong enough?

Weldwood is pretty good stuff and, from experience, I would say you have a 50/50 chance of success in using it. I built a Florida room for a friend who lives full time in Florida and had the same problem. I used Weldwood in putting up some of the moldings and, 10 years later, most of them stayed in place. I believe the ones that needed to be re-done were due to applicator error.