Knowing full well that I'm no major part of this community (lurker if you will), I say this with baited breath: this isn't a job! It's a fun competition and it's a damned shame to see people's hard efforts going to waste if their maps aren't even going to be submitted in a complete state, even if they don't win at least they won't have any regrets.
What I'm saying is have a small extension, a two week extension, anybody who isn't anywhere near to finishing; still isn't going to finish and people near completion if they work their buts off will be able to hand something in. People who've finished by the original deadline can spit polish their work to perfection.
When the prize/reason for most people will be just the knowlege that Valve has looked at their piece of art - then let them submit it at it's best.
Also Valve Time... It's freaking traditional!