I have gotten my Mooncup to work brilliantly now. It has taken me quite a bit of time and a bit of research. But fortunately I didn't give up easily.
I have a pretty low cervix early in my period and it is also quite heavy on day 2&3. Wearing the Moocup in a comfortable position meant that it was sort of sitting on my cervix and leaking a lot. If I tried to wear it low enough I got no loeaks but it was very uncomfortable because the bottom of the cup was sticking out (and that was with the stem completely cut off.

I found a forum specifically for menstrual cups and got lots of help there. My doctor said I don't have prolapse or anything, so that isn't an issue. Someone suggested weaering the cup inside out. That would never have occured to me. But it makes it just that little bit shorter and with a "squarer" bottom so that I cannot feel it at all when wearing it and I have no leaks at all.

I'm so stoked that it is working now and thought I'd share it here in case someone else can benefit from that tip.