Stephen -
I hear you on the wind. Since I don't do this for a living, I have the luxury of just not cutting if it gets very windy.
I'm generally not cutting anything huge. My firewood cutting is usually 6"-14" DBH, with most in the 8-10" range. I do occasionally get something bigger.
I like the idea you mentioned about putting a hand on the tree when tapping the wedge in. I'll try that next time.
John Mc