The majority of those flights were obviously with *A...
The US Airways ("US") program "Dividend Miles" seems to allow claims for past flights up to 6 months old... so may be the better option?
BTW you don't join the *A as such... you join the FF program of a member airline... but you can credit all eligible flights to that program...
I belong to NZ's "Airpoints" program fr'instance - and have credited flights from a whole bunch of *A airlines in the last 12 months.... It may seem surprising but I wouldn't recommend that particular program without knowing your future travel plans and what it is you most want from the program... "Airpoints" is...
unusual...