Comp ropes are there to compensate for the weight of the hoist ropes when the car or counterweight is below midway in the hoistway. There should be no problem doing all 3 at once if you can keep them from crossing. One at a time is slow and safe. Pick your poison.

I personally would put some weight in the car to get it close to balanced to the cwt and then remove the comp ropes and fix the sheave.

You could do the math to see worst case with the counterweights at the bottom how much the three ropes weigh per foot x length of comp ropes and just add that much weight in the cab.

Lots of ways to do this. Hang all three reels on a pipe in the pit. Car at top of hoistway .Remove cables from cwt. Remove cables from comp sheave. Shackle up cables to cwt. They cant cross unless you remove them from reels. Run car down to pit. Using car to sling from, repair comp sheave. One at a time, reeve cables through comp sheave. Shackle up to bottom of car. I have done this on 30+ floor elevs and never crossed a rope. When cables were babbitted on the bottom of the car, It was a little trickier.

Johnny has the right and safe way to do comp rope replacement.