Jim-
I can provide information on a few rivers. In 2006 I put in at the base of the Flaming Gorge Dam and took out at Hite on Lake Powell 456 miles and 23 days later. The Green River above the confluence with the Yampa (in Dinosaur National Monument) is mainly dam release so there will never be enough water for your boat and there are significant rapids. The Yampa is essentially un-dammed so during spring run-off there can be a significant amount of water flowing adding to the volume of the Green and more as you pass the Duchesne, White, and Price Rivers. The Gates of Ladore and Yampa within Dinosaur are both very popular whitewater river trips and require government permits issued via lottery that are nearly impossible to get. Once you exit the Canyons of Dinosaur it’s about 120 miles of flat water until Desolation Canyon (south of highway 40). You would be forced to exit at Sand Wash which is the beginning of 84 miles of spectacular Canyons including 60 or so class I-III rapids, and that road is far too primitive to trailer your boat and below there also requires a permit. Once you exit Desolation and Gray Canyons there are a few more rapids and a run-able diversion dam (once again our tugs are not the correct watercraft) before you reach Green River State Park at the town of Green River, UT.
Green River State Park has an excellent campground with showers and concrete ramp. Heading down stream, there are 68 miles of river (30 miles until you enter Labyrinth Canyon) until the only takeout and that’s a dirt ramp at Mineral Bottom (very scary road out). Permits are available on-demand at the State Park. This flat water section of river is a world class canoe trip year round but during spring run-off there is enough water flowing to support larger boats.
Every Memorial Day weekend (river flows permitting) there is a well organized power boat cruise beginning at Green River State Park through Labyrinth Canyon, on past Mineral Bottom, continuing on through Stillwater Canyon to the confluence with the Colorado River (120 miles downstream). There you’ll turn upstream for around 50 miles to a concrete ramp with paved road at Potash or another 12 miles to the ramp at Highway 191 in Moab. This trip can only happen during spring run-off as there will not be enough water the remainder of the year and there would not be any power boat support. South of Mineral Bottom (on the Green) and Potash (on the Colorado) you are deep in the Canyon Lands and there are no roads or services of any kind down to the river. Below the confluence of the Green and Colorado Rivers is Cataract Canyon. Both rivers contribute nearly equally to the size of the river through Cataract and there are 25 miles of world class rapids. Depending on the level of Lake Powell there will either be lake or river to Hite which is the first road you’ll come to.
Here you’ll find information on the Friendship Cruise:
http://friendshipcruise.com
Realistically, you would be putting your boat at some risk to do this trip. I would consider doing it in my R21 but it’s so slow it would take several days to do the upstream leg of the trip against the spring current (I’m also intimately familiar with both rivers). And, I have another boat designed for this purpose I can take on down through Cataract Canyon.
Those are the only possibilities north of Lake Powell. Below Glen Canyon Dam there are 16 miles of flat water with a paved road and concrete ramp at Lees Ferry. Although I’ve done the 300 miles through Grand Canyon (another difficult permit and very large whitewater) into Lake Mead many times, I have yet to do this short section of river. From what I understand it is gorgeous canyon and one could spend a week there in what is essentially the beginning of Grand Canyon (really Marble Canyon). That section of river almost always runs clear so at slow speed, one could spot the submerged boulders. I met a gentleman with a C-Dory at the Lees Ferry ramp as I was launching downstream last May.
If lake Mead ever returns to near full pool one can head up the Colorado through 50 miles of Grand Canyon to Separation Canyon. Currently, at these low levels there is a new waterfall that has made upstream travel there impossible and illegal.
The San Juan arm of Lake Powell contains more spectacular Canyons rich in archeology and early American history heading east. At full pool one can experience this rare beauty up to Slickhorn Canyon. But since the late ‘80s this is another permit controlled easy whitewater trip (84 miles) beginning it Bluff, UT and ending at Clay Hills Crossing. At current lake levels there is a sizable waterfall that has developed several miles below Clay Hills.
I might add that it’s a really bad idea to attempt any of the possible sections (or any river for that matter) without a secondary form of propulsion.