The bank cards in question are Coil on Module. You can’t attach an antenna to them, they need to be paired with a separate board. The end result will also end up being as big as the contact interface, which is anywhere from 9.5-12mm wide and rigid.
Most credit cards can’t be converted with the conversion service, because the bare silicon is attached to the back of the contact interface and covered in hard resin. The antenna connections are not readily available to be connected to and every card would need a different antenna.