There are a couple of products out there that utilize rapid heat exchange to cool the athlete and improve performance. I can dig a little if you would like, but it seems to be a pretty well proven concept.
As far as your questions, this is just off the top of my head. PM me if you want to talk about anything more.
1. Are you asking whether results would be more reliable if you had the subjects perform the protocol more than once? (Probably would). Or are you asking whether doing the extra volume of work, via the second Fran, is going to produce more beneficial results in terms of fitness for your clients (you'd think so).
2. Depends on what you're trying to test. I'm assuming here that your hypothesis is that this equipment is going to promote more rapid recovery between bouts of intense exercise, when compared to no treatment. If I were doing this, I'd probably have each person perform the same back-to-back protocol at least 2x, and randomly assign them to receive either "treatment/control" or "control/treatment". You could have everyone perform the protocol a time or two beforehand to prevent any improvements just from learning. Anyway, you get the idea.
3. It would make intuitive sense, but you'd have to find a way to test it. It's possible that the increased volume at that intensity could lead to a state of overtraining, which would blunt the positive changes and increase things like cortisol, etc. I'm sure there are plenty of folks here who will chime in on this.
4. I don't think that taking that type of break between intense protocols would be "un-crossfit". But that's just me.
5. Couple of ideas:
a. Make it a competition, and find some competitive folks.
b. Pay them.
c. Film them. (and post it)
d. Bring Annie, Nicole, and/or Eva in to smoke them. Or just to yell at them, and tell them that last rep didn't count.
e. Bring Coach B. in to tell them that they "will become born again hard". And then glare at them a little. (yaaaaa, burpees!)
Hope that helps out a little.