Lets review.
You are getting a lift, you want to have the door open when truck is on lift, you have 12foot ceilings, you have cathedral type trusses. You need to lift the truck about 6 foot to work comfortably under it. You have 10 foot tall doors.
Questions.
If you have cathedral trusses, how high is the peak? Are you "married" to the idea of jack shaft openers?
Summary.
You can get door track systems that allow the door to open and "hug" the angle of the cathedral ceilings. I have one of these and it was roughly 75 bucks more to purchase. These door track system allows you to use a conventional overhead door opener. If your walls are 12 foot, you are going to have plenty of room to have the overhead door open while the truck is on the lift. I have 10 foot walls with cathedral cieling and I measured 5.5 feet from the top of the bed on my Tundra to the door when it is in the raised position. (my structure is the same size as yours)
By the way Free Willie, your pic needs a bit more reference to properly visulize it. I'm pretty sure you have the same system as I do except my torsion spring is attached to the header. And I'm trying to catch you on the # of beers, I got another hour with the time change and all

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KO