There are jobs that just seem to get messy and can be a real pain in the butt to do. I would put gluing back down veneer on our Beaver cabinet doors in that category. I am visiting my sister in-law in Napa CA and she was a cabinet maker for many years. I had a door where the veneer panel edges were raising up anywhere from two inches in to a half inch most of the way around the panel. She lent a professional hand on her method for handling this repair. We used a high strength wood glue similar to Tightbond 3 in a Elmer's version. It was a little thicker in consistency and set up a little faster than Tightbond. Either brand would be fine.
She cut a half inch plywood piece to fit over just the veneer section. She pulled out a tool I had never used, a palette knife. It was offset, very thin, and made out of very flexible metal. The blade was about 3 inches long and about 1/2 inch wide. What was great about it, is that you could use that pallet knife to move the glue around in all areas where the adhesion was lost...great thin flexible tool. She then put wax paper over the veneer panel, then the plywood, we then clamped the plywood with a couple of 3/4 inch pieces of hardwood on top of the plywood and a blocking on the backside to protect the finish. We clamped to force out the excess glue, wiped that away, folded over the wax paper where glue had gotten on it and we then reclamped.
After an hour, we pulled the clamps and boards, then we worked the pallet knife around the edges to remove the excess glue. Some damp and dry paper towels finished the job. This was the best experience I have had regluing veneer and it was because the palette knife was the perfect tool for this job. The wax paper also kept the glue from getting on the clamp boards and sticking. This was the closest version to the palette we used that I saw on Amazon.
http://www.amazon.com/Kemper-Offset-Palette-Knife-P47/dp/B00DJFT8EM/ref=sr_1_119?s=arts-crafts&ie=UTF8&qid=1442617141&sr=1-119Some photos of the knife at work. Hope this helps.
Later Ed