My primary thought is that it is better to have 1 ok landmark games then 4 landmark games where some people like some, and others don't like them.
This concentrates everyone's effort onto the same problem, making it a more active and interesting thread...the more people are collaborating together the more fun it is. If there were 3 or 4 of these threads in here tomorrow, I would probably stop participating.
With that said, I don't see anything wrong with retiring the old contest and modifying the rules for a new one...I just think that people should try to come to a moderate consensus first.
Personally, I don't have any problem with the present set of rules. I did mention that I think the most fair way to choose hints is to just have the hint-giver give hints whenever it is convenient for them, but I don't think that sort of thing needs to be mandated as a rule.
I think that 24 hours is way too short. This isn't the only thing to do on the internet, and if they got automatically killed in that very short period of time...it would just make it easier to say "nah..dont know it, I'll just wait for it to die" and pretty quickly nobody is even taking the contest seriously anymore.
However it does make sense to have a worst-case resolution strategy. Worst case: someone posts a picture that is impossible, then wanders off and never gives hints anymore. So it's my suggestion that there be designated hint-intervals. You must give a hint within the first 2 days, then 1 hint per day until completion. If you go 24 hrs without posting a hint, then your landmark is forfeited. This would keep the game from dying.