[neilw20]

It is nice to have things perfect, but with my big CNC lathe I have been too lazy to test/adjust/test/adjust the tailstock.

Even if I got it right aligning the axis, it is serious work getting it correct to the correct height if it is wrong which it probably is.
On a job using the center I just do a test run and make a part, then add fudge factors, like a small taper into the program.
It makes perfect parallel parts all day and I still have clean hands.

Similarly I make parts on the SX3 and fudge the program for any errors, and just document them,
such as overshooting 0.032mm bringing the head down for a final cut, and backing off the 0.032mm to allow the head to settle at the correct Z height.

Even on large machines I have had had to compensate for Z final height in this manner.

Until you replace the Z strut with two 20Kg struts instead of one 60Kg strut you will have very significant Z repeatability issues, which gives an unexpected cr@ppy finish. With the strut at one side, as the head travels down the tip of the cutter has a small X+ error
and when you move the head up that tiny bit the Y+ error (due too sideways tilt) is removed.
Now when you go up you get a X- error. If the cutter is against a left face it will gouge slightly as you retract. You need a Z0.05 Y0.05 move for example to stop this gouging.

There are similar Y- Y+ errors. It will gouge on the face of a pocket nearest the front of the machine on a Z-UP move. Just document and fine tune the program.

As for rotating the head square, the spring loaded alignment pin works fine.
Just put the ahead back to vertical, grab hold of spindle with left hand and tighten the rotate lock nuts. That fudges it dead square.
You know when it is square. Surface milling has even criss-croos cutter marks. The error from head tilt and springing causes causes the criss cross error to change, and as the table machines across the X-Y range you can notice the table tilt as it over hangs either side.

The tilt in the X-Z plane means if you cut along the length of the table it will cut high in the middle. As the table goes off center the heavy bit hangs down and the other end pushes up slightly.

Of course, on my SX3 which has a quill and a Z micrometer it is really easy to fudge a small z compensation without a program change. I love my quill and readout. The (useless??) readout should not be pooh poohed. It is useful.

I have found the squareness of the machine (my SX3) to be fairly good and the deflection errors were much more significant in practice.

If you start measuring, flexing of the column and various parts become obvious, but for something that only weighs this much I just live with it.

I am doing jobs holding a Z tolerance of 0.01mm ALL DAY (on stainless steel) using a few fudges in the program to make a silk purse out of sows ear.
Ya gets what ya paid for, and its all not that bad when CNC can fix it.