That looks like a great setup!

If you align the ST to make it square with the BB presumably you clamp the BB down with a bolt through the middle and yank on a thick tube inserted into the ST. But what bends when you do that? Don't you just end up with a slightly curved ST?

My approach which is a bit redneck but bear with me is to weld the BB shell to the ST completely first, before making any other part of the frame. I get it as square as I possibly can: best possible fit-up (easy because it's the first joint), tack it, check it, and weld it out completely. It's usually very close. From that moment on the BB shell takes no further part in the alignment process and is not used as a reference. I make the ST and HT parallel to each other, ignoring the BB. The rear axle is then positioned square to the plane defined by the ST and HT and centered on it. This should result in a frame that's well-aligned but with the risk that the BB shell isn't absolutely square to the centre line. But because the cranks and chainrings and things aren't very long a tiny error here makes very little difference. A small angle between HT and ST will affect steering and any error in the rear triangle is magnified to the point that the tyre looks in the wrong place. Neither outcome is acceptable. A small error in the BB shell is the least worst compromise.

If I used the BB as a reference I would risk magnifying any small error there to where it might become a problem. Once welded that joint isn't going to move so it seems that correcting it will just result in a bent ST and it's not clear that that's better.