I would recommend offering a 2 week extension, but give those who've done theirs on time a bonus point or two.
Nick has tried with previous contests to offer early bird bonuses, newbie bonuses, etc to increase participation. They look good on paper, but when you look at how they've been implemented there just is no real benefit when the scores shake out--the bonuses are negligible, rarely enough to differentiate between rank, just a little expanding of whatever gaps were already there.
We all had the same deadline. We all got ample advance notice (in June) of Nick's travel which lead to the previous extension. At this point, we can all offer up competing excuses for why we didn't get 'er done, so to speak, but the plain and simple fact is, this is a contest and failure to show up on time with an entry would get you booted from just about any other imaginable contest on the planet.
As I noted in the direct reply to Nick, I think anyone not meeting this deadline should be competing for consolation prizes/leftovers after those that showed up on time were awarded appropriately based upon their performance.
In my case, I've got the write-up ready to submit. If I had a couple more weeks, I would have built a different design, more complexity, done a more detailed write-up, been a lot more competitive. If the deadline's extended at this point, I've got the option to scrap out what I've done and rework/enhance it. Had this come up a few hours later, I'd have already entered and be stuck. Extending this late in the game is just not fair, period.