Interesting. I can't say I've done them all but I wonder if the Phoenix type really exists. Are there any brave marketers out there willing to sacrifice resources to "fail fast in order to succeed"? If there are then I wana be your friend =D
On the Eureka type, I find most of my ideas coming to me minutes before I fall asleep. Certainly not in the shower and definitely not in the loo (I know some people get great ideas while taking a crap). It can be frustrating for me sometimes because your mind is super active and you tell yourself you'll keep it in your head. Sometimes, just to get it out of my head, I type in a draft SMS and send it first thing in the morning (that way they'll be like "galing! pinagisipan mo talaga all night!")
Collective and Peace Treaty might just be the opposite of Eureka. Your idea, if the group collectively agrees to it, becomes the idea of the whole group. Good or bad. If its a good idea the whole group parties, if it turns out to be bad, they blame it all on you (lazy shitheads).
Well, whatever the type of idea you come up with, it's always good to have a mental challenge. The worst thing you can do to yourself is give up on creativity.