I am getting ready to upsize my attic joists and I would love to be able to remove everything and get all of the demo done and have everything open before installing the new joists and supporting walls below, but I don’t want my walls to push out in the process. The house is 22’ x 28’ and there is no ridge beam. The rafters are all 2×6 and the pitch is 12/12. The new joists would be installed within a day or two of removing the old joists and there won’t be any live loads or snow loads on the roof. 

What would be the most efficient way to get the old stuff out while still keeping the structure from being affected?