If I had them, I'd use a round bar in a collet rather than a chuck.
I'd use the longest bar that I had, as the longer the bar, the more accurate the achievable alignment. If I had some straight tube I'd use that for preference, but it would have to be closely round tube, not oval.
I'd then mount a dial gauge on the saddle. I'd then check that the bar was straight by setting the dial gauge at the end of the bar furthest from the headstock and rotating the chuck by hand. I'd also check at a couple of intermediate points in case in case the first reading was at a null point on a banana shaped bar.
If then the bar proved to be straight, I'd take dial gauge readings along the bar by traversing the saddle.
Adjustment to the headstock by splitting the difference in traditional form. The headstock to be bolted down to a known torque between adjustments.
This all assumes that the mis-alignment is only in the horizontal plane. Given the risk of dirt trapped beneath the headstock, distortion etc. I'd also check alignment in the vertical plane by setting the dial gauge on top of the bar and repeating the alignment check along its length. If there was a problem there, I'd weep and then bang my head on the headstock until one of them was properly aligned.
By this time I'd be in need of a cuppa or a beer.
What have I missed?