Welcome Rps, I recently acquired a '05 myself that is getting brought back to life. The carbs are worth sending to Ducatiman, even if you are familiar with cleaning them. These 250 carbs are tiny and take a bit more to get spotless than others.
I've transported bikes in the short bed tacos before, I would just put it in straight and leave the back wheel on the tailgate. It should work unless you have a toolbox taking up bed space. Diagonal would work too but I'm a stickler for aligning my ratchet straps in such a way that the force is directed symmetrically on either side of the bike. Not to mention, when you load the front suspension with straps you are not left with a lot of downward force on the rear wheel. I do one strap around the rear wheel just to keep it kicking side to side. Here is a pic of how I moved my SV in a much older truck, yours will need the tailgate down of course:
