With your truck being 4-dr 1 ton dually, you have a pretty good base to work with. The problem is not wanting a crane on it permanently mounted, and I truly understand not wanting to do that on such a nice truck. What you may do, once you settle on what type of crane, could be to tie into the truck frame under the bed at say ... the right rear corner, and sandwich a steel plate in the bed bolted thru to the underneath structure. The inside of bed plate would not be unsightly when the crane was not on it and not have much effect on normal use of the bed. Of course, this would be more than a screwdriver/channel locks kind of fab job.
I don't have the problem of not wanting to mess up a nice daily-driver truck. I have a bucket-truck, and added a permanent crane to it's right-rear utility-bed compartment on top. I used an Autocrane 3203, like you see on highway service trucks,etc. I didn't put it on for logs, but it will surely do them.
A small jib crane should help you, mounted correctly.....don't want to screw that Ford up....
That setup on the white truck looks like it'd work. Inserted into the reese box and the crane offset. What I'd do with that setup is add an outrigger/tongue jack to the area at the crane base and make the crane post swivel. You'd have a 2-point mount (hitch & the ground). That pic looks like the whole structure swivels solely on the hitch?