Play on casual
Go into map, use left and right d pad to highlight the trucks to see if any have the medium log carrier
Drive up the left hand side of the map
Hit the fuel stop
Hit the log shack
Back down the same way and across the bottom to the lumber mill, nice easy drive, rinse and repeat till complete.
If you want to big brain it, this is how I got it, same method, use the K700 that spawns (often near your starting garage) to tow the medium log carrier up to the shack, following the same route as above.
Load up the medium carrier, then use the manual advanced log kiosk to spawn 3 medium logs, use the loader on the back of the K700 to grab and hold these, lift them as high and as near to your cab as they will go.
On casual the logs clip through the surroundings so you don't need to worry about collisions, at least not while they're so far up and out of the way.
Tow the other truck with the medium log carrier to the mill, unload it
Then reverse the K700 and unload the loose logs it was holding carefully and nice and straight onto the medium log carrier.
Swap from the K700 to the other truck, secure the logs, then unload.
Done in one trip.