I do the pedal fast in low gear but I try to go as fast as I can and most or at least 50% of the time I am as fast as the stop and go traffic.
I also go on the sidewalk in rush hour times- not fast, super slow and always give pedi's the right of way, sometimes I pedal backwards to alert them (its not illegal in my town to go on sidewalks) sometimes even getting off my bike- big deal, its a hell of alot better than being stuck in my car, and I am not super rushed ever.
Most of the time it is residential streets- just be super aware and wave some cars by you if they are trailing behind you.
I also do not wear a helmet. Studies show that cars are more cautious around non helmeted bikers. Rest of the time I am on bike paths.
It will take a season or 2 to get into shape- off season weights help big time.