That is very nastily hilly ! Wonder how messed up it would be to even walk the bike up that hill !!! But being a regular commuter I can totally imagine how mentally demotivating it could get to get up that hill day in and day out.

I will say one thing .. The OP asks if he is just weak for averaging 10 mph on good and 6 mph on bad days -- No way ! Just being able to ride the bike on hill like this is an achievement. 6mph is not bad at all. It is a very decent speed. And besides, being a regular commuter, I would say this - DO NOT fall into the "how fast am I going" trap. It will lead to burn out pretty soon. It is commute. There are good days, bad days, and then it could be raining on bad days and stuff like that. On a hill like that, I would even consider walking your bike for very steep sections if you don't feel like it every once in a while. It will still be better than driving !