One I've considered is to temporarily suspend down voting after submitting a story. But this has some unintended consequences in that it unfairly penalizes the people who submit heavily, who provide a lot of value to the site.
Your assumption that people ordinarily upvote submissions they like isn't necessarily valid. I usually read the site pretty passively, and only upvote things I think are really spectacular. It doesn't mean I don't like the other things I read, just that they didn't really blow me away.
"counter to the idea of upvoting" is a pretty vague phrase. Counter to your idea maybe, my criteria for upvoting fits my idea of upvoting just fine. Not everyone thinks of a vote the same way, as another story on the front page right now points out, this is one of the problems with a site like this.
Neither! I'm assuming one _can_ exist. I think I have an idea on how to make it work; I just don't have a forum to test it on, yet.
It's not hard to implement downvoting in a way that doesn't have the problems you described.
Also, I would assume that people ordinarily do upvote the submissions they like. The only way you could be describing anything different is if you meant that you upvote everything that you don't dislike, which I think runs completely counter to the idea of upvoting.