I had a nice long chat with my new good friend "Al" from the AA RTW desk (my second time working with him on this ticket).
The problem was not with the re-route, but with changing my first flight out of Sweden. I was originally going to leave on March 11, but I wanted to move it to March 10. This, apparently was the problem.
By keeping that same flight on the same day out of ARN and flying on the 8:30 PM deprture to DXB, I was able to make the change, nab the extra miles and points and notbe charged extra.
All in all, I can't really complain.