Another easy way around the phase cooldown is to break up the group and then rejoin. I have had to do that a couple times to keep from having to wait around.
However, when dealing with PUGs expect the unexpected and nothing will ever be easy. Even if you know exactly what to do and have done it 100 times that way, someone will argue to do it their way or else. I got told how to heal HM EV the other day, saying I was a terrible healer. Sorry my healer is a little weak and I can't heal people through getting a lava waterfall shower...maybe better if you don't stand with you back to the lavafall. Sure some Sage could heal you through that.