Once the insides have been removed back to the frame, and before the roof decking and roofing materials are taken off the timbers should be accurately measured and tagged for re-assembly. The tagging needs to be recorded onto a set of plans prepared after the frame has been exposed and measured. Then the roofing can be removed and the roof decking; bracing off as needed as you go.

When that is done, then you dis-assemble it usually by figuring out what was put up last and take that down first. Working back to the foundation by removing rafters (with or without purlins) then plates, and then lay down bents and take them apart.
Each piece should be inspected for damage and or rot and noted on the previously prepared plans.

All timbers should be stored someplace dry, like a storage trailer for moving to the next site.

At the next site the timbers can be removed from the storage trailer, and repaired as needed. Modified as needed and readied for re-assembly. When ready, re-assemble into structure again.

Years ago, the guild held a workshop showing how to do such a thing and we learned how to measure an existing structure, create the plans, tag and record, then dis-assemble. Months later we were taught how to repair the damaged timbers, and re-erect the frame.

It was a very nice learning experience for all who attended. I was one of those who was there.