When the cut is open stay clear of The Narrows!
Check craigslist in metro areas around the lake, like Phoenix, Salt Lake, Las Vegas, and even Denver.... people are offering to share their houseboat time shares all the time.
Also check http://www.ksl.com/
Check the bulletin boards over at http://wayneswords.com/
for general information and discussion. Several people over there on that forum have been on Lake Powell since it was created. Wayne Gustaveson is crazy knowledgeable about the lake!
ARAMARK, the park concessioner, is the only authorized entity that can do rentals on Lake Powell. If you look online you will find several other companies that also supposedly do rentals, but they all just act as a middleman and end up going through ARAMARK. If you rent a boat from someone else be advised that it is not on the up and up and you ARE taking a risk!
You can get a free trip to the lake for a week if you want to pick up trash, check on the Wayne's Words forum. I did this and it was very, very fun!
The best times to go to Lake Powell are late spring and early fall. The monsoon storms are over and all, or most of, the school kids are back in school! I went to Lake Powell for a week once in late September and never saw another person on the lake after the first day!
If you go to Lake Powell bring at least one extra prop and all the tools necessary to replace the prop underwater. In my Powell kit I carry two of these:
The water clarity at Powell changes greatly depending on how far north you are the lake. By Hite the water is very muddy, but by Page the water is pretty clear and you can see pretty far when underwater. My crew just bought a dive hookah for our next trip to Lake Powell.