What we've been doing is sort of a software sandwich with a human filling. Software does a first pass through all the stories to guess which ones might be good candidates (otherwise there are too many for humans to review). Then humans pick some candidates. Those go into a pool from which software randomly picks one every so often and randomly places it low on the front page. After that it's up to the community which ones are interesting. The ones that aren't fall off the front page relatively quickly. I've been meaning to write some code to collect data on how much frontpage time they get.
That's the current state. We do still send repost invites occasionally, but mostly not, because users made it clear they don't like the duplicates.
I don't think the human phase can be automated. Instead, our plan is to open it to the community, so it isn't just us and selected users picking stories. The challenge is to design a mechanism for that which doesn't just reduce to an upvoting system (since as the knight in Monty Python says about the grail, we've already got one it's very nice).
We'll also probably publish the list of stories selected in this way, whether or not they end up getting traction, because if nothing else it's alternate reading material.