installation of a new steering rack

I am replacing the steering rack on my 2013 Prius C One. The steering wheel is on center held by the seat belt. When I got the old rack out (by dropping it together with the cross-member) I saw the match marks on the shaft and bearing did not line up (about 120 degrees off). I checked the old rack and confirmed that it was not centered. Mark lines mark the centered position. I am the 1-st owner and never touched the rack before. The new rack that came from the factory is not centered either (confirmed by the dealer). The new rack has no markings to indicate the center.

My plan is to center the new rack (all the way to the left stop, mark, all the way to the right stop, mark, and split the total angle in half), and then try to jam it into the union while the steering wheel is straight. Is this the correct way or am I missing something? I am not sure why my existing rack was off-center. It is possible that I accidentally pushed the tie rod ends while working, but not likely. I had 12 1/2 turns of the outer tie rod on one side, and 12 3/4 on another.

Also, the instructions say to mount the rack on the cross-member first. It will be difficult to insert the shaft into the union with all the weight. I am thinking about putting the steering rack long bolts in, then inserting just the rack without the cross-member into the union (just hang the passenger side by the inner tie rod using a rope), and then lifting a cross-member and trying to line up the 2 steering rack bolts, engine moving rod (horizontal large bolt) and other 6 bolts at the same time. Do you think this is a good idea? Or should I mount the steering rack first onto the cross-member?

Thanks.