Presumably, the bike computer would have measured moving time only at the slower speed as well. In my experience, idle time on my commute is a constant, doesn't matter if my average moving speed is 10 MPH or 20 MPH, I still hit the same lights and stop signs and wait approximately the same time every commute.

I'm not doubting the 10 minutes shaved off the commute time, and I don't doubt the average speed of 14 MPH, but I'm a bit skeptical that clipless pedals and a more aggressive posture would result in an increase of 40% in average speed. I'm guessing the OP was averaging a bit higher than 10 MPH prior to the changes.