Pyno&dyno,
Better pictures would help for evaluation - for instance a photo taken straight along the barrel (not at a slight angle, as in your first photo, at the start of this thread)
As far as I can judge, the foresight is about 10 degrees off vertical in the clockwise direction (looking forwards from the breech end).
Now, if you look at first of the 2 photos you attached yesterday, it seems that the register marks on the barrel and the action line up to much better than 10 degrees - maybe to 1 or 2 degrees. This is difficult to judge, because you took the photo at an oblique angle (and once again, it would be better if you made a photo that was absolutely vertically above the register marks, so that on ecould see the alignment more clearly).
I doubt that Bubba made those marks after fitting the barrel incorrectly. So I suggest that you take a very close look at the foresight block and the ears.
Do they show signs of being mishandled with a wrench or clamped in a vice?
Do your very best to remove the foresight assembly. I think you may discover that the FORESIGHT assembly is skewed, not the barrel!
As as been pointed out, quite correctly, if the barrel was seriously out of register, then one would expect trouble with extraction. But you say that the rifle shoots OK, and has been proofed in Italy(at the Gardone proof house, I imagine).
Now for the benefit of those living in a country that does not require proof by law in an official proof house (i.e. NOT just a manufacturer's proof!) the proofing does not mean just ramming in an overloaded cartridge or two and seeing if the gun will take it. My understanding is that the proof house will also check the chambering/headspace. In fact, they will do this before firing the rifle at all, to make sure that the marked chambering is actually what is in the gun (there are enough unmarked/wrongly marked/rechambered guns around to make this precaution necessary). And after passing the proof test, the rifle will be marked with proof code, date, and the actual chambering (if that is not already stamped on the action). My local dealer showed my a barrelled action that had been rejected as unsafe by the proof house without being fired - they really do check first.
At least that is supposed to be so in Germany, and I have no reason to think that Italy is any sloppier in this respect. But the proof house will not check anything else that is irrelevant for safety, such as the alignment of the foresight.
I therefore think that it is conceivable that Bubba wrenched the foresight at some time. Maybe trying to remove the barrel? Maybe trying to align the foresight? Maybe the key is missing from the keyway? Who knows?
But I think you should do the easy and cheap thing first - get that foresight off and take a good look - before (possibly) wasting a great deal of money on refitting a barrel that (maybe) does not need it. The trouble may be in the foresight assembly itself! Key missing, foresight twisted???
At this point, you should beg/borrow/steal/copy the book by Charles Stratton "The Pattern 1914 and U.S: Model 1917 Rifles" ISBN 1-882391-29-2 so that you can learn how the rifle is assembled. That would be your best investment right now, before spending money on anything else.
And I recommend making two better photos (see above) and posting them here - I may be completely wrong!
Patrick