Nope, Carol, I proceeded in the "dumbest" way possible: no hassle, nothing. I just set up the Gmail IMAP account using the default "Gmail" icon offered by iOS, and that's it. Contacts
are syncing for me. No idea why they wouldn't sync for you.

Are you not offered the option is iOS settings? I definitely am, for every Gmail account I have set up here. I'm on the most recent iOS 6, and this works for me both on the iPad and iPhone.