Some of the "trails" and the 4x4 jeep trail east of Buck Rock a motorcycle is better, IMHO.
Photos towards the end of this message.
Most of the dirt roads I've been on would be OK.
Except where a tree might have fallen over trail last Winter and not yet been cleared (which sometimes doesn't happen for a few years).
On the regular old paved and dirt roads there are many locations where you can turn a truck of any size around.
And, I don't think boondock camping is encouraged outside of the designated camping spots (dry or otherwise), I've never seen it done.
A fair number of hunters in the area in the Fall, as well.
- - - - - - - - - - - - - - - - - -
Here's some photos from a past trip.
Typical old pavement...
Typical dirt roads...
A few spots are like this...
And, this...
However, both of those were beyond the tree we found a few years ago...
It would have been hard for a truck to turn around on this trail.
Kings Canyon proper is just to the right of this photo and about 1,500 down slope.
- - - - - - - - - - - - - - -
Here's the Jeep or 4x4 trail, east of Buck Rock.
It was just up and down, up and down, up and down, sometimes a little better condition than this section, sometimes just a smooth granite surface.
- - - - - - - - - - - - - - -
So, I think you'll be OK, except on some of the smaller width trails and the 4x4 trails.
You decide.
Maybe drop the camper and have some fun on the 4x4 trails?
- - - - - - - - - - - - - - -
And, lastly... just for fun... the Happy Honda Trail Riders that I often ride with.
The low and slow, yet steep is not a problem... "go climb a tree" bunch.
For the Ride Report, if you are interested...
Kings Canyon & Sequoia, 2009.
Here's a photo of a campsite at Unit 5, Big Meadows, before I got my ATC Bobcat.