It was interesting centering the work in the 4 jaw chuck; I wasted a good amount of time adjusting it in the wrong direction. With more practice I expect it will become more intuitive.
I just used the tools and compound angle that the PO last used, so if you see something wrong, please shout.
That looks like it would be a PITA to center. I have not done a lot with a 4 jaw but have progressed a bit with it. Not afraid of it anymore. I think a ways back, I would have referenced off of each edge of the square base. But my first impression looking at your set up, I wonder if this would work....? (more a request for input rather than giving advice)
That particular project is not super critical that the piece be centered, although a good opportunity for practice. Would it be acceptable to center punch the center of the piece after scribing diagonal lines, then use the tailstock as a pointer? Put it very close and visually, you could see what jaw actions are doing to the piece alignment. I would think that you would get within a few thousands and since the purpose is to flatten the bottoms, not drill an exact center hole, would that be a suitable set up procedure?
Otherwise, how does one center a square sided piece with cast edges like that? I think I saw someone on Youtube pull the pointer of a dial gauge back, rotate the piece, check, pull the pointer back, etc. And those edges are cast edges so bumps here and there?
Or should one reference off of the back of the jaws?
Any suggestions?