Ohhhh! Use BOTH legs when pedaling! (face palm)
 

It's something I've noticed in the past, but today I really worked on it, I made sure my left leg was doing the work too. Actually, to me the way it felt was the left leg was doing more work, but I'm sure thats just an illusion brought on by the right leg normally doing most of the work, and now having an easier load.

My average speed went up 2 mph, hills were easier (still hard, just not as hard), and I would say my ass and back gave out before my legs on this ride.

Also, I better understood the term "spinning". When using both legs more equally and pulling up as well as pumping down, the ride felt much different. My legs felt better and I went fast with seemingly less effort. Spinning as opposed to pumping.

However, my butt and back hurt more as I spent less time leaning on the pedals for support and using them to drive me forward instead, if that makes any sense.

I still hurt right now, but it was a good day.

I too am right leg dominant.
When I first got back into cycling, it took some decent concentration to get both legs to put out the same effort.
After a while, muscle memory builds up and you forget about it.
I try not to pull up too much, as it led me to an ankle injury that took a good couple months to stop bugging me.
Instead of trying to pull up, envision trying to scrape mud off the bottom of your shoe at the bottom of each pedal stroke.
It will help keep you turning to cranks smoothly in nice circles.

I've heard the mud scraping thing before, I don't quite get it yet, but I think I will in time.

Get yourself a set of rollers. That'll fix those uneven pedal stroke problems right up. ;);)

CRUEL!!!! I was guilty of one legging it mostly for a while too, then I started doing spinervals and using toe clips.. started using both legs in a hurry!

Spinning refers to a high cadence, not necessarily to the "shape" of your pedal stroke. There's no fixed number where you're suddenly spinning, but to me, 90+ is generally spinning. 100+ is definitely spinning.