I also had to completely trim off the stem. I seem to be fairly 'short' and it sounds like you're describing where the stem was out and the base of the cup is right there.
The other thing that was suggested and makes a little sense, is the condition of the pelvic floor muscles. Our little one is just a year old and I know those muscles are still pretty bad. Doing Kegel exercises will help strengthen those muscles and seem to help keep the Diva Cup in place. I've been using it four months and each month it seems to sit in place a little better. I tried pushing it up a bit higher, but realized the top can touch the cervix and I can still see the bottom. I swear the cervix gets higher as my period goes on... Anyways, later in my period it sits much better.
If I were you I'd get rid of the stem and work from there. Definitely a 'work in progress' for me!