Use a solvent to dissolve the plastic from the card then epoxy the extracted antenna and chip innards to the back of your phone case. Problem solved. (I'm only 50% joking, you can actually do this but maybe epoxy isn't the best option.)
replySomewhat similar, Polar sells a band with an NFC payment chip in it (no experience, just saw it the other day):
replyOther solutions that use the same underlying technology:
replyI'd like to do this, but epoxy it to a dress watch
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