Thing about the suite is that it isn't ONLY given out to park visitors. It can also be used for promotions (the first actual family who stayed there was in Ellen's audience and chosen from there), or really however they choose. There's no equal chance 365 days a year, many days are blocked for promotional reasons.
But other than that, the Dream Team is, as far as I understand it, told where to go and at what time by a computer choosing those things randomly.
That said, I was told by a CM who gave us a magical moment (preferred seating for Billy Hill) that with Dreams, the earlier in the day you get there, the better.
As for it not being fun to try to spot the DT, whatever! It would be less fun to purposely NOT look for them, or to ignore them, than to have the fun of keeping an eye out for them.
We wouldn't have gotten the magical moment if I hadn't noticed the CM dressed awfully like a DT member (I believe she was, but just wasn't on orders from the computer at that moment, so she had her jacket on over her vest) and purposely walked by her, gave her a big smile, and said good morning. She chose to reply with more than a 'good morning' back, we got into conversation, and voila, magical moment given.