I know that depending on the woods and dimensions, when you go big you really need to use the proper glue or changes in expansion can cause the veneer to crack and do other undesirable things.
From my research I found that its rigidity is actually one of the properties of hide glue that make it great for veneer. When it dries, it is rock hard and experiences no creep. From my research, I read that its rigidity is also what makes urea formaldehyde another good option for veneer. PVA glue is very flexible in comparison, and contact cement is even more so, and the flexibility can eventually lead to issues, especially with wood veneer on horizontal surfaces like table tops. That is probably not as big of an issue in the vertical context for this project.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.