Being that River Permits are over the counter right now, why not just get a permit and run the whole thing?
If you want to paddle downstream of Pearce Ferry, take the bluff road turn off at the old town Pearce Ferry structures and park at the bluff over Pearce Rapid. It is a short hike to the Pearce Ferry Rapid(which is sizably smaller now that the lake is affecting it) that you can easily portage on the left and paddle the 18 approximate miles to the lake. It's not the inner canyon but it's a beautiful float nonetheless. If it's remotely windy at the bluff it may be howling on the lake.
rrshuttleservice.com would probably be happy to run your car around as they live in the meadeview area
If you do decide to run the Diamond Down section (which I highly suggest
call Moenkopi Riverworks 928 526 6622, or one of the 3 other outfitters and you can hitch a ride down to Diamond Creek on someone elses takeout shuttle. There's no need to take your car down the road if you don't have to.
rrshuttleservice.com can take your car to the other end?