Tons of great info everyone - awesome thread.
So I'm back from my trip and it all worked out very well.
The second night it rained heavily then snowed heavily.... according to the staff at Madison campsite the weather scared off some people. They had a ton of cancellations, then most of the sites rebooked right away.
Ended up 2 nights camping at Madison.... then the 3rd night a few hours south of Grand Tetons
Saw bison, a grizzly, a black bear, deer, etc.
had a wonderful time.