I have a house built in the early 1960's where the previous homeowners neglected the garage completely. The garage is approximately 22x22 and has 5 ceiling joists running front to back that have either cracked or sag between 1.5 and 4 inches. On top of those I have 2 running joists running right to left. The garage is unfinished and many studs were bad so I have already sistered new boards to all of the existing studs or removed the ones that had serious damage, but now I need to tackle the ceiling joists.

Originally I was planning on sistering the new joists to prevent further movement, but in for a penny in for a pound so I thought I would install all new joists and remove the old ones. Unfortunately when I went to put the new joists in b/c of the sag and the right to left braces I am unable to get the boards into position. When I lived up north we had jacks that supported our floor joists in the basement.

Question?
Would using a jack like this be an acceptable way to raise my existing joists so I could get the new ones in place?

What would be the best method off attaching the new joists? Standard nailing or lag bolts?

Since I live in a hurricane area I would prefer over do it rather than under do it since my breaker box is in the garage and runs thru the uncovered breezeway.

Any help would be greatly appreciated.