Could the OP split the tickets?. If each pax has their own reservation number then each pax should have individual control over the chauffeur drive.

Just so that EK knows that you are trvelling together the OP can call EK after the booking is split and ask them to put a note on the tickets.

What I am not sure is if there will be any issue at checkin ( due to different surnames) if checking in separately.

I remember doing something similar ex LGW while travelling with my parents . Had to split the tickets to upgrade them to J as I didn't have the miles needed to upgrade all three of us to J at the same time and was not sure that the seats would still be there after a week. ( while I was waiting for my spg points to come to skywards)

While logging into the EK website using the different confirmation numbers we each had the option to book the car separately.