No need to pull the doors.
I use a couple small electric winches hooked to the rafters in my shop.
I use one for the drivers side and one for the passenger. They are spaced on my rafters at cab width.
If you're using a loader or forklift just make sure you space the straps on the forks so that the straps are pulling straight up and not "pinching" the body. It probably wouldn't cause damage if it did pinch some, but its safer to avoid that additional stress.
Open the doors(and rear windows on an ex cab). Run a flat loading strap through the cab. I then close the door with a piece of thick rubber between the door and body to leave a gap, and use a few pieces of wide painters tape to hold them "closed".