I am actually pretty anal attentive about torque sequence. We had an improperly torqued part at work that caused loss of aircraft when it went so I see the sequence as a big deal. I usually torque to 5in-lb first in a cross sequence. Then repeat at 10, 15, and 20 if necessary.
I will torque all the bolts on one cap to the first setting (5) before doing the same for the second cap, that way I'm not breaking sequence on the first cap.
I torque to angle on my cap bolts, until the final torque setting is achieved, and that is to spec. The reason for this is because when you torque to spec in increments, you will end up shifting the caps. Think about it this way. Picture top left bolt as 1, top right as 3, and bottom left as 2, and bottom right as 4.
Torque to 1 is 5#, followed by 5in-# to 4, 3, and then 2. Now, you've got compression already occuring on the tube here, and bolt 2 is going to travel further in on that 5# than the others, because all torque is, is a measure of tube compression. Bolt 2 is benefitting from 5 inches of torque, from 1,3, 4, PLUS the 5 in-lb you apply to IT.
Does this make sense? Maybe not just looking at the surface of it, but why not take feeler gauges and insert them at the corners of the ring caps, and I think you will see what I mean. Numbers are all correct, but that cap isn't sitting flat. Torque to Angle and final at torque to spec tends to result in less variance, here.
I also fully tighten one ring cap, and then move to the other ring cap. This insures that any distortion of the tube caused by tightening the rings is not magnified by a factor of two, as whatever distortion of tightening ring cap 1 occurs is null, and we only have distortion from ring cap #2.
Distortion...wtf man? Okay...you are compressing the tube, usually by about 20-40 thou of an inch in my measurements...well...what happens when you compress a tube's walls circumferentially? It either stretches, or shortens. Those are its two options. I prefer to only battle the stretch/shortening ONCE, which is why 1 ring cap is tightened at a time, so that only 1 ring cap is applying this stretch to the tube without "give" from the other, vs. BOTH ring-caps simultaneously stretching the tube without give. It is my opinion that final distortion on the tube is thus less when 1 ring cap is tightened, and then the other.
All of this is MY level of OCD and minutia, and none of that explains your absurd POI shifts. I honestly cannot explain the huge shifts you're getting unless you used different ammo, which you claim not to have.