I found the diva cup to be extremely uncomfortable when I tried it (not while diving). I move my period around by skipping the placebo pills in my pill packs. It's the most convenient way to deal with the problem. In fact, sometimes I skip them just because it's easier to not have a period. Obviously this won't work if you're not on birth control pills.
OK, I just want to say that this seems like a grand idea, however, using any type of prescription in any way other than the way it was intended can be very hazardous to your health. Please don't recommend it to others. I am in the medical profession. I am not trying to slam anyone, but without consulting your OB about this practice it can increase your health risks.
I have used the cups before and I liked them better for flow control.