The difference is not that high. In fact, my understanding is “Visa Signature” and “World Mastercard” (which are most of the premium credit cards) normally cost about the same as Amex. At worst it may be about 1% more not double.
The payment processors I'd be looking at offer merchants rates of 0.125% for girocard, 1.39% for VISA/MasterCard, and 6.2% for AMEX.