As I understand the rules of road racing, the King of the Mountain points apply as long as rider and bike reach the top... It doesn't matter if the bike is ridden, pushed or carried. So, why hold yourself to a higher standard? So it is possibly Matt 3, Bridges 0.

However you compute your points on this one, good luck on your next attempt! I rode a hill recently that I have never ridden up before, so it can be done, and I understand the challenge to make it... and at 315 I am not an elite climber either.