likely, every grower of bougainvillea and other softwood species, has his/her own technique to preserve deadwood. the bottom line is, if whatever you do works, then stick with whatever that is.. I don't think there is a BEST technique. a lot depends on where you live. climatic factors like seasonal changes, temperature, rainfall, humidity, make a difference. most important is the condition of the deadwood as you begin to work on the tree. if you create new deadwood from live tissue, your deadwood can be surprisingly durable. if rot is advanced at the outset, especially if it goes deep inside the trunk, all the punky wood needs to be removed down to hard wood or the decay will continue to the point where your tree is a goner.
this is what I do. allow the deadwood to air dry after you carve and sand. torch the wood to further dry and harden then wire brush to remove loose ash and fibers. saturate the wood with oil based stain, sometimes several coats. allow sufficient dry time then treat with wood preservative. teak oil, tung oil, minwax wood hardener, thin super glue and other similar products all work. currently I use carpenters glue diluted with water to facilitate application. the glue drys clear, stays somewhat elastic, and seems quite durable, especially if one applys several coats.
regular followups are vital. hope this helps.
best wishes, sam
LOL I know pots for this size tree must be very expensive and hard to find. 
