I'm clipless challenged

I'm not sure what you are describing here.  You've unclipped, but still fall?  I assume before you used clipless you used platforms or cages, right?  Once you've unclipped, it is the same - put the free foot down as you lean to that side (so you don't end up down on the clipped in side, which can be very embarassing). Or is it a matter of still trying to move the foot forward instead of planting it straight down? That might mean you are still pedaling on the clipped-in side, and automatically moving the free foot.  Stop doing that.

Thats exactly what it seems like.  For some reason I keep a lot of weight on my clipped in foot.  This wasn't a problem when I was on platform pedals because I was on a bike entirely too small and could reach from the seat.  Silly really.

I think I get nervous that I'm not going to get my foot down soon enough so I try to do it too early. 

OK, that makes more sense. Trust yourself to put the foot down.  It also sounds like you are on a larger bike (or at least are higher up on the post), so you are maybe still getting used to the height as well as the clipless pedals.  If you are unclipping early, make it a point to stop wherever you have unclipped, even if it's 20 feet from where you meant to stop.  If you are too far back, try to scoot up to where you need to be, or let yourself coast if possible without pedaling.  You might even think about drills on an empty space (school parking lots are good this time of year) where you practice unclipping and stopping or coasting then stopping.

I still get nervous with mine also.  I figure the more I get otu there, the better I will get.

My first couple of rides, I unclipped both sides, just in case I leaned the wrong way.  After a while, I realized it what side my body preferred to support me after I unclipped.  It ended up being opposite from what I expected.