That's like, literally impossible? "Hey I just invented ameliuspay, your shop doesn't support it, go directly to jail"

The closest you have is SEPA because it's universal on all Euro bank accounts. And many webshops do offer it. It doesn't integrate into credit card workflows because it's a push payment - you have to go to your banking app, type the details and send the money, while the website waits. Some people might have to go to an actual bank.