A couple of thoughts:
1. I do like the idea of HYO coming back. It's been long enough and the site has calmed down enough that it's worth another go.
2. I like the idea of minimum post count AND minimum time since a user has joined the site to be able to play in an HYO. If you have just a minimum post count, then someone could come and post "I agree" a bunch of times just to play HYO. If you have just minimum time, then you could have someone who created an account years ago but never contributed at all here trying to play HYO.
3. I'm sorry, but 12 hours is too short a time frame to force people to respond. Nothing wrong with encouraging that, but if, for example, someone sleeps for 8 hours and then has an early flight the next day, they might not be able to check the site. This is especially true for the host--they may be able to check the site but it can take longer for them to post something, as it takes time to check their script, format their post with the graphics, etc. A 24 hour time limit, on the other hand, is a good amount.
3b. For the mods' sake, I don't think you want them having to take over shows even if the host disappears for a couple of days. That sounds like a lot of work for the mods, who have to look at someone else's script, try to use their graphics, etc. Instead, I'd vote for a rule of if a host goes silent for 3 days, their show goes on hiatus and we start another show. Then when one of the ongoing shows finishes, the half-finished show can pick back up. And then the host is not allowed to host another show for at least 6 months unless they had a *really* good reason to abandon their show in the first place.
4. I of course agree that there should be a variety of hosts, and that they should have to submit scripts in advance. Perhaps there could be up to four shows going at once--two by new(ish) hosts and two by veteran hosts.