How to get Amex without changing Aadhar pincode?

I currently live in an Amex non-serviceable area and will be soon moving to Bengaluru. I just rented a house there and planning to apply to Amex. However I came to know that Amex card needs pincode of a serviceable area in our address proof. I don’t have one. Should I change my Aadhar to my current address.? (I don’t want to) but if there aren’t any other options then I will do it. Hence asking the good folks of Reddit for a way around it.

PS: Please do not DM with the Amex referrals. I already have many dms in my inbox for the same.