Wow, you guys are most generous with the information, so much so that I started to think this is a no-go for me, paint the back plywood panel. But then, I figure that why not try it, if I screw it up all it's going to cost me is the price of another 1/4" plywood from big box, and some paint.
I'm still thinking about type of glue to use, will study all your comments above as well as the videos provided, and any YT videos I come across. One thing for sure, per suggestions prior mentioned, I'm going to cut the big sheet into 3 strips for ease of handling. Studying the veneer, I've found 3 places where it looks exactly like a multi-board glueup. I'll do one at a time letting the glue dry for 24 hours, three days in a row.
Thanks for all the comments.