fwiw, owlmaster, i am a big believer in higher cadence. my own experience is that i go as fast or maybe slightly faster spinning at a higher cadence in a lower gear. on my road bike i rarely use the large chain ring. btw, my cadence is around 95 rpm. on my road bike. with spd pedals.
without the clipped pedals i doubt i could maintain that kind of cadence. even so, though, i think i could spin somewhere in the 80s. to me anything slower would feel, well, too slow. i'd highly encourage you to experiment with lower gears and spinning faster. it sounds like you've begun that by using your 6th gear. i suspect that if you feel you're going slower it may be psychological. is your entire commute time the same or longer when spinning higher in a lower gear?
also, i want discourage you from riding the sidewalks. i think they are more dangerous than the streets since a car or truck pulling out may not be expecting to see a cyclist. you are far more visible on the streets than on the sidewalks. as pointed out elsewhere, it may even be illegal in your jurisdiction (as it is in mine). sidewalks are for kids on bikes, not adults.
good luck on your cycling adventures!
** mp **