OK.....I also should've mentioned the curved arch is 80 1/4" wide and peaks at approximately 39". I tried to "force bend" a regular sheet of 1/4" Sapele plywood and was within 4 inches of succeeding when the piece began to crackle.
The problem with veneering the piece in place is the task of managing a 10' long contact cemented limp sheet of veneer (paper backed) without having it make contact somewhere. The same holds true of veneering on a flat surface such as my bench, but the handling problems become more manageable.
Lastly, I don't want to appear ungrateful for the advice or argumentative, but I don't understanding if the outer most skin of a 3/8" flexible plywood substrate is nothing more than a thin layer of inexpensive wood veneer. Then why would one more thin veneer layer automatically immobolize the flexibility of the flexible plywood substrate?