I thought:
1/ replacing a parts of the plastic cover with a cooper plate,
2/ drilling the platic cover (once removed) and glueing a circular piece/plate of cooper,
but, after reading closely your post, I would say that it is highly uneasy to do because of the rectangular rubber rim and two plastic pins which are pressing and the battery either the SIM-card.
I´m not a craftman only a human looking for solutions to unreleavant problems 