Hey Runnin Rat! I'll tell you my husband's trick that helped me stop falling, because the falls that you're describing are exactly like what I experienced. I would stop, clip out and have the bike's weight leaning away from my clipped out foot and over I would go. When you stop, try turning your wheel away from the foot you've clipped out, i.e. clip out right, turn your wheel to the left. Here's the reasoning: if you stand over the top tube of your bike with your feet on the ground and turn your wheel, you'll see that the weight of your bike naturally falls the opposite direction of the way you turn the wheel. Some gals find that doing the opposite of this works (turn wheel toward your clipped out foot), so you could try both and see what works for you.

Where in NV are you? I grew up in Las Vegas.