Do you have a stigmatism? Contacts offten don't work well with people of stigmatism.
With not-so-bad astigmatism, you can get away with not correcting it in your contact lenses. That's what I currently do. It works okay and brings you to a good level of vision (1.0 here in Germany, probably 20/20 in the US).
The shifting position isn't a problem, I think the bottom-heavy ones adjust fine with a little bit of practice, but the experience is never that good.