My hypothesis is that it'll probably come out roughly equal in the wash. Most callers try to make their evening of dances so that no one gender is doing more "work" than the other. At least that's what I do. For every gents allemande 1 1/2 there is another dance with a ladies allemande. Generally. Of course there are more ladies chains than men's chains, but I figure there are usually enough gents-only moves that make up for it. Especially if you are going for a long-term experiment. And I guess that depends on who you dance with too - looking at dance 9, which should have been the same dance for each couple, but one couple had the gent with more steps and the other had the lady with more steps. Perhaps one couple flourished more than the other (and most flourishes have men spinning ladies?). Maybe there was role-switching going on? I don't know if you're going for strict science here, but doing things like extra flourishes, role switching, and things like that will definitely skew the results. You're going to have to control your conditions if you're going to get an accurate reading, otherwise you might get results that don't tell you much. Though you do assume normalization amongst dancers - one extra twirly dancer will cancel out some of us fat lazy dancers who don't twirl as much. ;)

Could you help define the chart? For each dance you have two numbers for lead and two numbers for follow. So that tells me that you have four different people wearing pedometers for each dance. I am quite fascinated by dance 9, where one couple has the man with 100 more steps and the other couple has the woman with almost 200 more steps. Presuming it was the exact same dance, I am wondering how that could be? To be sure you normalize, you're going to need to balance out those who flourish a lot with those who don't flourish very much, or use only non-flourishers, or use only flourishers. Seems to be a lot of degrees of freedom.

You might consider using the Weight Watcher activity measures. Also you could have more than one pedometer on the same person to see if there are differences and average them out. Some dancers have a weight watcher activity measurement devise or pedometer, and would bring it to the dance.
The other measure you could get is a heart rate monitor. A lot of people have this. It would be great if you could get one that record the heart rate chronologically.
The other thing is you could contact the http://www.cooperaerobics.com/Cooper-Institute.aspx
group and see if you could work with them to figure a method and devises that you would need to measure it. They may be interested in dance as it is a social activity that may be more appealing to some than traditional exercises. They are a non-profit like you.
Some callers alternative between fast and slow dances and between different types of dances. It would also be interesting to note differences in dances.
It may be useful to measure heart rate at a certain level and also calories burned based on heart rate and movement.
Some moves like ladies chain may have a lot to do with how the person is turned when the reach the other side. It takes more energy to turn the person into place than to do an overhead twirl.
The research may lead to a better understanding of contra dance as a form of exercise and how to make the most of the workout.

It would also be useful to interview people on how they were injured to see if there are methods to reduce the accident rate. You could have an online data form to record injuries. And the best methods of dealing with them.

I wore a pedometer to several dances in a row during a month of counting steps for a work contest. Each time at our local Thursday nite dance (8-11pm) I clocked 10,000 steps, +/- 300 or so.