Using a unique email address.
Using a unique physical address (both for my account details and for my delivery addresses).
Use a unique credit card (I'd probably get a refillable prepaid gift card, and set up some auto topup to ensure it's got my expected monthly Amazon bill available as "credit", but not much more).
I'd probably move any AWS billing to a different Amazon account.
If I were more paranoid (or being actively targeted), I'd probably also try to go unique on _everything_ I tell Amazon; phone numbers, different city/state/zipcode (as well as street address), company name, website url, alternate contacts - then I'd set up "Security questions" with unguessable questions/answers (perhaps diceware/xkcd style "correct horse battery staple" type ones, that a CS rep could easily read out and verify - rather than a base64 GUID...).
Not that I trust the "security questions", but if Amazon lets you use freeform questions as well as answers, it might help to make your first security question "Have you noticed this account has two factor authentication turned on?" with an answer like "Yes, so Amazon Customer Service will take additional care when being asked to reveal account information, right?"
Think about how many people actually use Amazon services
Through sheer competition, Amazon is forcing Walmart to close over 100 stores. We only know that because Walmart is big enough to get noticed.
Remember when Walmart was the company putting local mom and pop shops out of business?
Cycle of life I suppose...
2FA does not help here as someone goes through support channel which looks like bypasses 2FA
Also concerned if the same trick can be applied to Amazon Cloud services, as there one can also run up a big bill pretty quickly.