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.)

Somewhat similar, Polar sells a band with an NFC payment chip in it (no experience, just saw it the other day):

https://support.polar.com/en/payment-wristband

Other solutions that use the same underlying technology:

https://fidesmo.com/consumer/wearables/

I'd like to do this, but epoxy it to a dress watch