Hi @lewisjohnston
If you need to exert pressure on the SIM card when it is inserted, try sticking an appropriate sized piece of tape ''on the back of the card'' and then insert it.
Hopefully this will force the card to make better contact with the SIM reader pins due to the extra thickness.
Perhaps initially leave a "pull tab" as part of the tape on the back of the card, making it easier to remove in case it is now jammed in the reader due to the extra thickness of the card and you wish to remove it for whatever reason.