The different scenarios my imagination has come up with all end with you saying "mega bummer, dude".

I paid with cash in the end :) A+, would do again.

amex cards all have chip versions that you can request for free

Have the chip version of the Amex Platinum. Since its the US version, its chip and signature, not chip and pin, and works almost nowhere in Europe.

A lot of places wouldn't take Amex of any description; it's far less commonly supported than Visa and Mastercard.

For those who don't know, the term "coffeeshop" in the Netherlands refers to places that sell cannabis. "café" is a regular café.