I involve my Amazon in the process of assembling anything that requires assembly. From the opening of the box (this come easier if you allow your parrot to play with cardboard boxes), removal of the parts, to the assembly. Yes, this really slows things down and you must keep a close eye on small items like screws, but the fear issues just go away.
Never under estimate the positive advantage of touring your home every few days reintroducing your parrot to the home and where out of sight people are (find a family member game). The process takes the edge off of new things by placing them away from the parrot and with time moving them closer, especially if they are very fearful of 'new' things.