Abraham -
It is possible that the method you are using to measure headstock alignment is misleading you - for several reasons.
If you use a dial indicator with a standard ball foot to measure vertical alignment as you show in your photograph, you will only get a true reading if you have no (zero) misalignment in the horizontal direction. The reason is that any slight horizontal movement will call the ball to run down the side of the round bar. To avoid this you should get an 'elephants foot' for your indicator. This has a flat base and can tolerate a small amount of movement at 90 degrees and still give a true reading. The same argument applies to horizontal measurement.
The second issue you will have is that you must get a degree of droop in a test bar, just under its own weight. You can calculate this to subtract it from your apparent reading. This may be too small to worry about compared to your other problems. Droop is not an issue when measuring horizontally, provided that you use a flat bottomed foot for your indicator.
The third potential issue is with your test bar itself. It has to be very straight for the tests that you are doing. Ideally a ground bar is needed. you can check this within reasonable limits with a surface plate and vee blocks.
Fourthly, a test that just runs along the top of a test bar assumes that the bar is held straight by the chuck. Ideally I would do away with the chuck and use a test bar fitting in your spindle taper. These are available at a reasonable price. In either case you need to take readings with the bar rotated through 90 degree intervals, to find and eliminate the effect of the chuck and taper not being straight and concentric with the axis of the spindle.
Last, the test can be compromised by the TIR of your spindle bearings. You can remove this effect to some extent, but it could be significant enough to cause apparent problems over the distance that you are clocking your bar.
Can't do much about the flexibility of your lathe bed though
