I agree about the SJ permits. If you didn't enter the lottery this year, you would need to call and have them send you a paper application. Then you send in the paper application. Then you call in for an open date. Yes, it is really this prehistoric. Or you take your chances and show up at the BLM office in Monticello and hope that someone has cancelled. Their calendar has been very full this year. Look on their website for open dates:
http://www.blm.gov/utah/monticello/river.htm
If you plan to run the SJ, it really helps to get a camping permit from the Navajo Nation, so you can camp on river left. Otherwise, the supply of campsites can become very limited, with the number of groups on the river. These permits can also take weeks to get, or you can drop in to the office and pick one up.
The other issue with the SJ is that it has been running 5000-6000 for most of the past 2 weeks. It is a different river at this level, with riffles becoming actual rapids, and Government is a respectable Class III rapid. Eight-Foot and other rapids also turn into respectable II-III with holes that you really want to miss. In rafts or ww kayaks, no big deal. In open canoes or with novice boaters, it can be a cold wet silty experience. This water is coming from Navajo Dam releases, so you could call BLM and find out the release schedule.