Reddit has an endpoint where you can download all submissions. (however, due to the API limit of 100 submissions / 2 seconds, it took me about 1.5-2 months to get the 41 million submissions)
Have you looked at number of comments instead of number of submissions? That would seem to be a better estimator of user growth.
Honestly, I don't think that estimating number of submissions is a very good metric for the growth of Reddit (or Hackernews). If you want some proxy for its influence, you care about readership more than anything else. This thread [1] on Reddit (and the references therein) shows that 50% of Reddit activity comes from users that aren't even logged in. So even if you were just able to measure logged in users (which would still be a far greater number than submissions), you would still only estimate half the influence.
Honestly, I don't think that estimating number of submissions is a very good metric for the growth of Reddit (or Hackernews). If you want some proxy for its influence, you care about readership more than anything else. This thread [1] on Reddit (and the references therein) shows that 50% of Reddit activity comes from users that aren't even logged in. So even if you were just able to measure logged in users (which would still be a far greater number than submissions), you would still only estimate half the influence.
[1] http://www.reddit.com/r/TheoryOfReddit/comments/1khp85/logge...