How about doing this on a demand basis, ONLY when somebody asks?
Wait for the request. Bypass FAA altogether. Take the image to a local printer, where you receive the print personally, sign it, and ship it yourself, after payment for the order, of course. And charge appropriately.
As others have pointed out, FAA does NOT offer an option to receive a signed print, nor does it offer the website interface to pull this off. It's just not part of the game here, so no real love lost for handling it all yourself, since business is business.
If you start getting lots of requests, then just start doing or redoing all your uploads to include an unobtrusive signature, since you would have decided that your market wanted this. This is not the same as a live signature, of course, but it might suffice.