Some trucks have two exhaust pipes sticking up above the cabin instead of one. Examples are GMC MH9500, Mack Pinnacle, FLD 120 and 6900XD but there are probably more. As long as what's too long for the back of your truck fits between the exhaust pipes, you can have it extend over the cabin and beyond, resting between the exhausts that keep it from falling off to the right or left, even without a crane. You only have to support the rear of the cargo and stop it from sliding off the back, which any sideboard bed does naturally.
Screenshot 2:
On the 6900XD, even with the roof rack on, I found a 3-slot sideboard bed can be used for 6 long logs. The exhausts I was using (the ones that for this truck are farthest apart) needed a half log's width more space between them for the best fit so the 6th log sat on top of the others a bit, but it still worked well with careful driving.
As a bonus, logs never get stuck in the sideboard bed and you can always grab them from the side because in the middle they are in the air.
In the truck customization menu there are exhaust pipes that are farther apart or closer together, and their height varies too. Six long logs may not be the limit, especially without the roof rack I was using. You don't strictly need to give up your trailer hitch and use a 5-slot semi, adding unpowered wheel axles that cause drag, to do a modest(?) "sideboard shuffle". (I also had other reasons to not use a semi for the particular journey in screenshot 2.)
Screenshot 1:
Taken when I tried it for the first time. The cargo is Large Pipe (Cargopocalypse contract, Alaska) with a length of 4 slots. Instead of the rear mounted crane that stops it from sliding off the back, a 3-slot sideboard bed would likely also have worked here. It was still able to freely pass under the Alaskan pipeline overpasses. You can see one on the left.