* If you can, take the train into work. That's about 1.5 hours of additional productive startup time. Sitting in a car is dead time.
* Get rid of your lunch hour. Park yourself at a nearby Starbucks and add an extra hour each day of productive startup time. Do this every day.
* Given your spouse's variable work schedule, my guess is that your most productive time is in the evening, after kids are in bed. Can you shave off 2-3 hours per night? Better managing this time is huge.
There may be other things that are specific to your family life that can give you 30-60 minutes here and there. Time slicing like this is hard, but it adds up to meaningful startup time.