I've read some horror stories about foreign travelers getting scammed by merchant, and then Chase backing the merchant. Amex is supposed to be the best at backing the cardmember, but all of my three Amex cards charge a foreign transaction fee.

Of my card selection, which tends to be the best when it comes to dealing with scam charges and doesn't charge a foreign transaction fee? Or, do I just bite the bullet and pay the 2.7% with Amex?

My no-FTF banks are:
Capital One
Chase
Discover

(I would just use cash, but I'd have to open a new bank account now that BofA no longer lets you withdraw cash for free from Global ATM Alliance partner ATMs.)