Dan
I've read through this thread several times and "IF" I'm reading things right, an answer hasn't quite been given to your question.
First off it appears that you are using a 3 jaw chuck on a lathe and want to center drill the end for additional support. If so, then your description seems to be doing things a little backwards.
Once a piece of round stock is chucked and the lathe is turned on, it is quite common to find the work piece turning off center... that wobbling thing we all know so well. Disregarding Bob's caution about uneven chucking, it's best to lock the metal down enough to prevent it slipping or worse... climbing out of the chuck..... that's a bad thing.
Once the piece is chucked, mount the tail stock drill chuck and a center drill. Run the center drill into the end of the work piece and watch how it reacts. If it is not offset, the center drill will begin to drill a hole dead center of the rotation, turning off small twin spirals of swarf, indicating a nice even cut.
If the tail stock is offset, the center drill will do one of two things. It will visibly move to the center which can be seen in the movement of the bit or flex in the tail stock bore. It might also begin cutting a small circular ring with a high point in the center. Either one indicates that you need to check the tail stock alignment.
Assuming the center drill begins a nicely centered hole, continue to drill until the larger part of the drill's taper is cutting metal close to its shoulder. You now have a center point that will accept the live center without having to bang anything into anything else. Replace the drill chuck with a live center and you are ready to true the work piece.
Yup....center drilled and the wobble is still there. That is what a lathe does.... it remove wobbles. As you begin cutting the long side, the work piece will become concentric with the center drilled hole and you have a nice stable surface to work with.
Easy.... safe and far more effective than trying to manually locate the center before locking the chuck.
Now.... if I missed the point of the question, then all bets are off....LOL
Steve