SO,
after reading all that, this is what I would do
I would forget about all the programming bullshit, and “go analog.”
Can you do me 2 things,
- scan your card with TagInfo, and check
EXTRA - IC Information- Capacitance: ???
- Use a bright torch / flashlight from behind the card to shillouette the chip and share the image
IF it looks feasible from the above information
Find yourself a wrist band you would like to use, and there is a reasonable chance if you grab one like these, it will have the correct antenna in it.
Or find yourself a suitable antenna from elsewhere
- Throw your card in some acetone, carefully remove the chip and antenna from the remains.
- De-solder the Chip from the antenna ( Put the antenna aside for later, if required to refurb)
- Solder the chip onto the new wristband antenna
- Test it
- Protect it as you see fit
- Insert into wristband
Job Done 
I haven’t gone into too much detail, as I have done something quite similar before, and its pretty easy.
But if you get stuck, or are confused about any part of the process, just ask.