Is it just that the ratio of submitted stories to people browsing new is too high, causing a low chance of any particular story to be looked at? If I had novel ideas on improving this I'd write it out, but I think others have already suggested things like randomly mixing new stories into the hot pages.
IIRC, the second-chance pool was our next experiment after that one. It has worked much better. The difference is human judgment or, if you will, taste.
It's not easy to come up with new mechanisms that might help with this problem. Every software mechanism we've tried allows many things through that don't pass muster. Community mechanisms, as soon as you open them up, get overwhelmed by people trying to game them to promote their own stuff. There's a feedback loop with that: the more interesting HN is, the more attractive it is to a high-quality audience, and therefore the more attractive a target it becomes for manipulation, which makes the site less interesting again. So there's a cap on how good it can ever get (https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...).
I know it took a long time for me to start looking at new, a little nudge would have made me start much earlier.
When you mixed new stories onto the front page, were they clearly marked as new or could they easily be mistaken for upvoted content?
Maybe this could be a karma gated opt-in feature that individual users can enable?
I feel good when a re-upped post or an invited repost makes #1, like Yayagram did yesterday, and Internal Combustion Engine has now (https://www.hackerneue.com/item?id=26991300), because that's such a strong indicator of the community finding a story interesting.