picked a handful of violets in my name

I get that gap too. It's hard to get rid of it - but once you've drawn your initial line, you can fill in the gap without worrying about your line being even. But it all depends on what kind of look you want/are comfortable with.

Harder pencils are terrible. They're just not compatible with soft eyelids. If you roll them between your fingers a bit, they should warm up and soften some, but they'll still be hard to get a nice defined line with.