<< >>>Looks like my method is still the fastest.
1) Call in first to file a claim and get a claim number.
2) Fax in all the paper works with claim number on every pieces.<<<
That used to work almost perfectly, but since Christmas, about half my claims have had to be re-faxed, and a couple still required snail-mail after they were re-faxed and 'lost' a second time. Because of this, I expect some claims will take 6 weeks from start to finish. Amex is receiving lots of faxes, and that has become an unreliable method of sending in claims for now, in my opinion. I decided to fax AND mail my last new claim in upon discovering that yet another older faxed claim hadn't been received. >>
I have a couple of claims pending and thought I'd call AMEX. I mentioned that I had heard there was some problems with faxes being lost and the CSR told me that she hadn't heard of anything like this. She did mention that they were taking a bit longer than usual due to the holidays, but they were getting caught up as quickly as possible and would try to get back to 2 week turn around.
My three claims were all received - 2 already have checks in the mail and 1 is still "in review" and should be finalized this week.... YMMV...