Welcome to the community and thanks for posting. So sorry to hear your Dad has been having trouble.
I'm not familiar with that particular system but I have a Virgin Mobile with a different manufacturer set-up and I'm able to do it. When connected via Bluetooth I'm then able to sync the contacts from the system itself. I'm sure the Volkswagen guy knew what he was doing though.
It's strange how swapping the SIM card allowed this to work because Bluetooth doesn't require a SIM to work. If you've got the contacts stored to the handset then you can try removing the SIM card all together and switching the phone back on and try it this way.
I'm not sure how a SIM card will help but it may be worth a try. You can call the team on 789 from a Virgin Mobile, 150 from a Virgin Media landline or 0345 6000 789 from any other phone. Alternatively, you can speak to the web chat team.
I'm curious to know how it all goes so please keep me updated.