Could you please posts transcripts (or at least the gist) of your conversation so that the other members may learn as well? (Don't be like Sam, LOL)
Let's make this a real forum discussion.
Besides that, what is one ply reversible? Is that simply white poly that has been dye-subbed black on one side?
If it is opaquely dyed, why would the print show through? Or are you more worried about where the ink comes through the mesh?
Also, have these already been done before by someone else? If so, could you get a sample from your client?