Hi Ross,
Cutting metal is the lowest order of the job. Work holding and alignments take precedence.
Of course this is entirely correct. I'm replying to you but my comment is meant for Volvo.
When I started off, I would (for example) line up the fixed face of a vise parallel to the X axis, then assume that the part I had clamped there was also parallel to the X axis. These days, as much as possible, I clamp a part then use test indicators to check the part's alignment relative to the axes. If it's close but not good enough, I typically loosen the clamping slightly (could be the vise rotation bolts for example, not the vise itself) then use a plastic-face or copper hammer to "tap" the part or the vise or the hold-down slightly, then check the part again and repeat before and after tightening. Machinists call this "clocking in the part". With some practice you can easily get parts aligned to 0.01mm along lengths of a couple of hundred mm. As much as possible, you should verify the "truth" of the part alignment with a test indicator just before you cut it. Typically you are checking alignment with respect to the X, Y or Z axes. Sometimes you are also checking alignment with respect to the spindle rotation or spindle axis or a rotary table axis.
In your case, when you have the head clamped to the angle plate and the angle plate clamped to the rotary table, you'll need to do multiple steps of this "loosen slightly, measure, tap, measure, tap, tighten" procedure, to get everything lined up, including the position of the angle plate on the table, and the position of the head on the angle plate. As Ross said, that setup takes most of the time. The actual cutting part is relatively quick in comparison.
If you can't get the part properly aligned with this procedure, then you have to scratch your head a bit, and modify your clamping setup. As Ross said, often this means putting in shims or scraping a bit off the part or adding another clamping element that can push or pull the part into alignment.
Cheers, Bruce