The old Dunhill Cup at St Andrews used to use what they called “medal match play”. It was a 3 man team knockout competition. So, three 1 v 1 games, each decided by the lowest score.
You could have six 1 v1 games each decided by the lowest net score to get the team element, at the same time each player has a score for each round for the individual medal element. (Personally, I’d do it using Stableford as that is a bit more forgiving and keeps everyone in the game which keeps it fun).