I've made several Catsheads, but have never put the screws/bolts out of array, from one another. If you keep them on the same plane, moving one should only affect its counterpart. If you put them 45* from each other, you'll be influencing both the Y and Z planes. Make any sense?
Also, if you can, look again at my above pic and try to mimic. The Catshead threads directly to the spindle. No need to center it in a chuck or other. I have other ones that are made to go into the Steady, but that's only for long work or difficult opps. The one-piece design, threading into the spindle, is bar far an easier to use fixture.
If you want to put the Catshead in the steady, you'll first need to center it in the chuck. Then, put the steady around it and get it running true (sometimes making a new register, on the OD, is needed.), while still in the chuck. Once good, open the check jaws and slide the whole thing toward the tail. Get the work centered in the chuck and slide the steady/catshead into place. Center the far end of work, in the catshead.