On my roadbike, I clip the left foot first, because my right foot seems more coordinated to get in while moving. I never thought about the added benefit of not tipping over into traffic until this very moment. It's something to think about though from a safety perspective. Most of the time I just trackstand after the initial takeoff. Speaking from the past now....but I suspect it will come right back. I can nearly do it again on my hybrid after a half dozen rides and no trackstand practice at all...just when crossing the city streets on the katy trail. Sorry you fell, glad you're okay.
God bless!
-Ron