1. Make this "HN selects startups which get invited for YC interviews", i.e., a feeder into the existing system. Essentially, use HN to supplement the network of YC alumni who help out with the application-filtering.
2. Since YC will explicitly still have the final say, open this to both Fellowships and YC Core applications.
3. Have a standardized form. Or possibly even a "make this application public" checkbox on the regular YC application form.
4. Use a more sophisticated voting system. I think a "which of these two looks better" combined with a form of Elo rating could work quite well.
EDIT: To the people voting this comment up: Do you agree with all four of those suggestions, just some of them, or are you voting it up because you like the fact that I'm offering ideas despite thinking that these four are all bad ones? As Dan has said a few times recently, discussion is more useful than votes. :-)