Is there any other way of knowing a player potential?
I would separate the groups and play as individuals in X-somes from time to time. Playing better ball would "mask" a golfer's weakness, especially if one golfer consistently gets the better ball in his/her group.
Is there another way of keeping score for our Golf group?
Mostly unaware of how "official" systems work (ie, GHIN looks official with respect to recording scores and calculating handicap), I would suggest the stableford scoring system for your group (playing as individuals). Stableford rewards better scores insofar that they have a greater reward than the penalty worse scores possess. "Player potential" would be observed through weighing the ratio of rewards and penalties.
If you need an "official" way to calculate handicap, perhaps stroke play can be recorded on the side. That would be a lot to keep track of, but this would freshen up the scoring among your group.