Put random new posts that don't have any votes on the front page of those who meet a high karma threshold. Currently a single vote in the new queue is a gigantic step towards hitting the front page and being noticed. When that one vote matters so much and there's so much luck involved in getting it before even newer posts come in, it's no wonder people are creating voting rings. I think this could hugely reduce the luck factor in quality posts getting noticed.
Here's a preview of what I'm imagining: https://i.imgur.com/ZNQTn7q.png
I would say that's newsworthy and worth resubmitting once, but by the current rules I'd risk being banned.
One problem with allowing people to resubmit is that they'll probably resubmit too much. It will also push non-resubmitted stories out of the new queue faster. The first might be able to be solved by encouraging the community to be responsible; the second by increasing the number of items displayed on the /newest page from 30 to 120.
There is another way to solve new queue randomness: create a page where submissions come entirely from HN members that each user may select. For example, I'd be interested in tptacek's submissions, along with tokenadult, cperciva, yours, etc, so submissions from those members are what my page would show. Each user would be able to select their own list of users that they're interested in. But this might be a bad idea because it will make voting ring detection a lot harder.
Another idea is to create a page showing submissions from members that you yourself select. I'd be happy with that, but that's a bad idea because it would divide the community. Pg's short experiment with highlighting users with high average karma proved that this is a horrible situation.