DEAR GOD NO! Please don't do this, most of us already have enough inboxes.
The only thing I like about non-time-series sites like HN is that it just isn't in their nature to ever be something inbox-like. It's the sole saving grace of having a voting system, especially with vote-ranked threaded discussion -- it keeps it from ever being something I have to "catch up with" regularly.
That's probably the most minimalist incentive you can give to increase New pageviews, and fairly easy to implement. (Edit: updated the original post with this suggestion.)
The only thing I like about non-time-series sites like HN is that it just isn't in their nature to ever be something inbox-like. It's the sole saving grace of having a voting system, especially with vote-ranked threaded discussion -- it keeps it from ever being something I have to "catch up with" regularly.