You're experiencing what seems like normal teething troubles. Your body is getting used to the cup; there's a good chance that this is causing the cramping and that it may go away by itself.

Many or most of us don't hear or feel their cups pop open. And Melunas aren't very poppy because of the material. They also tend to be oval in or right after use.

No, I don't think your cup is too big. It may be too small. Larger cups will, in most cases, sit around the cervix more easily, not on top of it like a hat; maybe your cup is hugging your cervix too tightly.
It also sounds like you could use a longer cup because it would be easier to remove... are you bearing down to move it lower for removal?

And it sounds like your cup is lacking capacity too.

Good luck! I know it's hard when you're struggling with the learning curve. Hang in there, it will most likely get a lot better real soon.

What m03m said. The medium Meluna, even the standard shape, is actually more of a "small" sized cup compared to others : http://sizecharts.livejournal.com/ We usually advise users with a high cervix to get a longer cup, and people with a heavy flow to get a larger, higher capacity cup because the Mini is actually one of the lowest capacity there is. So yeah, with a heavy flow, it could be overflowing. Or it could just be some residual fluid that was already sitting lower in your vagina.

But since you have those, keep practicing with them. It's normal for the cup to be oval, it's adjusting to your inner shape, but it needs to be fully unfolded and possibly (o) around your cervix. Unless it's really off-center, the cup should fing its way there. The cramping could indicate that it's not sitting correctly or rubbing your cervix, or there could be too much suction :http://menstrual-cups.livejournal.com/2091967.html
And most importantly, don't forget to bear down and "give birth to the cup" when you're trying to remove it.

I agree that your cups are too short and possibly too low capacity.

But get through the dreaded learning curve with them before spending more money on other cups that might not fit well. Figure out how to insert and remove them without ripping your fingernails off. Get to know what you like/don't about these. Then compare their dimensions, capacities and shapes to the 30+ other brands at http://sizecharts.livejournal.com/ or any of the other charts at the Community FAQs.

Yeah, if your cervix is usually unreachable, you're going to need a longer cup. The same thing happened to me a few months ago when I tried the 2-for-1 Meluna deal. If you like stiff-ish, maybe the Diva Cup would be a nice option, or for something very long and very soft, the Lilycup (which is now my cup of choice for all except my heaviest day)