Follow up. I decided to take one last shot at trying to resolve this issue by calling Goldman Sachs one more time this afternoon. The rep who answered this call was surprised to hear what had happened so far with my calls and said right off the bat that she didn't believe I should have to cancel my Apple card in order to update my email address. At first she was convinced that I *must* have had two Apple IDs since I had changed the AID email address last year. I never had more than my one AID account. So she looked deeper into this account. Though I had changed my primary AID email address a couple of times over the years, the original and official AID is an old @mac.com address, which no longer is a functional email address (because I wasn't willing to pay for it way back when Apple decided to charge to keep @mac.com).
Because my AID address can't receive mail, once I removed the address GS had on file as my AID, GS no longer had a working email address for me and that is when the paper statements started arriving. The rep today told me that emails to my previous address, though still a valid email address, have been getting bounced back to GS -- something none of last night's reps mentioned during all those hours of conversation.
Today's rep felt that if I went into Settings and changed my "reachable at" email for my Apple ID from the mac.com address to another working email, that change would propogate immediately to GS and they could resume email statements and discontinue paper. I already had my icloud.com email linked to my Apple ID, so I replaced the mac.com address with the icloud address (and left mac.com as a "reachable at" address on my account). As we'd hoped, the change registered immediately on her end, and she successfully sent me an email statement while we were still on the phone.
This resolution took many hours between last night and this afternoon, and I will need to re-sign in to some Apple services with my icloud address. But I won't have to cancel my credit card. It still does seem ridiculous that even though my GS account was already linked to my AID account I couldn't just update my email address (rather than actually change my Apple ID account's primary email address). And it would be great if the GS reps were all trained as well as the one that helped me today (though she definitely took me down some wrong roads before we hit on the solution that worked). She seemed as overjoyed to have found an answer as I was to not have to cancel my credit card and apply for a new one -- I think she surprised herself.
I figure it was worth typing out this situation in case anyone else runs into this situation. I would imagine it's not that uncommon -- or will pop up more often as time goes on with the Apple credit card) - that someone updates their Apple ID for whatever reason, only to discover down the road that they now have problems with Goldman Sachs, they start receiving paper statements, and so on...