Can I modify a slightly too big bike?
Try stopping with one foot down, leaning the bike over and leaving your dominant leg on the pedal with the pedal forward and up ready for a power stroke. By leaning the bike over you can get lots of clearance. I can often even remain on the saddle.

When you're ready to go, push off with your non-dominant leg (which is touching the ground) and give a strong pedal stroke with your dominant leg.  This will give you and initial burst of speed which will make balancing easier. Take a moment to adjust your position then continue pedaling.

I think frame stand-over clearance is a bit of a myth.  An older frame I use (older road bikes had very little clearance) has almost no clearance under my crotch and I really don't notice as I never find myself standing over the top tube.