If you clamp a DTI holder in the chuck you can bring the turret in and sweep round the ID of the drill holder and offset the X to get it centred.
A better approach would be to turn up an accurate bar to fit in the drill holder and sweep the OD of the bar, you can then also run along the length of the bar to check the alignment of the turret. Running along the length would actually be best as the first step as you can adjust the turret if needed then you can sweep the OD of the bar to find X centre. If the height of the drill holder is out there is likely not much you can do about that unless there is some way to adjust the height of the turret, shimming would work but could lead to less rigidity so I would only do that if it is well off.
Normally if you make up drill holders you would bore and finish them to size fitted to the lathe, first by drilling with a drill in the chuck then either a reamer or a boring head in the chuck to get to final size, that ensures the holder is exactly centre.
I have often thought of making a part catcher for my lathe but as I mostly do one off parts I dont really need it, would just be nice to have one for the occasional longer runs of parts.
Hood