Adam,
I have nearly always balanced my veneered stuff, except for smallish test panels and it is the received wisdom to do this.
Paul Richardson, former editor of F&C uses hammer veneering a lot and says that if you leave a veneered panel face down on newspaper to dry then it stays flat. (See page 76 in Furniture Making Techniques, if you have the book - publ. by F&C) I tried it once on a small panel and it was OK. (Hammer veneered stuff can take a long while to dry completely. I left it for at least a week).
I have no experience with very thick veneer., other than gluing a couple of similarly thick pieces of ply together and these stay flat after I have used my vacuum press on them.
I suspect a lot of the potential curvature comes from the drying out of wet veneer so if you used the iron-on PVA method, you might be better off. (I would never use contact cement myself).