Hi J.!
You're not neurotic! We have all these "experts" telling us what we should be doing and what our babies should be doing, it's enough to make any of us feel crazy and upset when our baby isn't exactly doing what he/she "should" be.
I gave my son a sippy cup at 6 months and he took it just fine. But I did some intense sippy cup shopping around! I ended up getting a sippy cup by Nuby. It has two handles on each side and a straw. The straw is wider and thicker than most sippy cups. I think that made it easier for my son to drink from it because it wasn't a huge difference from his bottle. It went right for the straw and started sucking.
I only find these cups at Wal-Mart and they're $3.96 per cup. Each cup has two colors on them (red/blue, green/red, yellow/green, blue/yellow, orange/yellow).
I'm not too sure about the crawling thing. The only thing I might suggest is putting her on her tummy on a ball (once of those big stability balls if you have one or one of those big children's ones). My son loved it, and still loves rolling on a ball at 14 months. Just a thought!
Good luck!