The one thing about our island holes is that players have a much higher chance of missing a 10m radius circle than tournament ball golfers seem to have missing their island greens. Seems like they miss maybe 1 in 12 to 1 in 20 depending on wind. It's not uncommon for our Gold players to miss 1 in 2 to 1 in 4. So our challenge and resulting penalties are higher to start with if both the shot and distance penalty is applied.
If this was the case, why not just move the tee forward? You would certainly then improve the ratio of players hitting the green. You might not achieve the desired scoring distribution (with too many 2s and too few 3s still) but you'd achieve your hit green ratio.
Or, why not expand the green size? What rule says that it has to be 10m in radius?