1st, be careful treating your commute like a time trial, it lends itself to poor decision making and wrecklessness.
2nd, dont bother comparing between your bikes on a route so short. Two miles is not far enough, so many factors at play here that any one of them could tip it either way. If you have any real concern try over 30-50? You will probly come in substantially faster on your roadie or the track bike than on a BSO.
If your commute is flat (13ft climb is pancake over 2 miles), weight will only really be a factor in getting the bike up to speed, once you get there, if you can sit on the gear, the gearing is fine. What sort of average cadence do you have?
I dont neccessarily recommend gearing down any further, I would say, perservere for a while longer, pushing the harder gear will improve certain aspecs of your cycling, your power output will increse (its strength training, and it will become easy given some time, bearing in mind this is not the only important thing to consider so maybe dont ride that bike all the time), once that gear becomes easy, you will spin it faster and faster.