Currently "gravity" pulls stories down as a function of time. If time were replaced by a counter that increments with each story upvote across HN, gravity would be normalized for activity and timing would matter less.
You mean instead of "seconds since this story was posted" it should use "number of stories posted since" ?
Sounds like a pretty good plan.
Though as other people mention you could also add pageviews in the mix, as well as "number of comments since". I'd say a nice linear combination of all three, softmaxed between some limits, added to the number of seconds. The latter bit because you wouldn't want things to go crazy when a huge amount of pageviews or things are posted.
But it's a good idea. Especially since I'm in a non-American timezone, which means that if I want a story to be seen I need to take into account US office hours as well, and your suggestion might sort of take the timezone effect out of it.
This could cause the unintended effect of making it impossible to get to the front page when there is heavy activity. It would cycle quickly between new articles. There needs to be a fixed time element.
An increase in the number of stories submitted already makes it harder for an individual story to get on the front page, since it rolls off the New page faster.
I think I know why you didn't like the story-upvote count, since sometimes there might not be any good stories available to upvote. But keep in mind that if story upvotes are the new "time", then "time" slows down for the existing front-page stories as much as it does for the new submissions.