Alaska has gone to a 2-tier mileage pricing on domestic award seats, 12.5K miles one way (economy) and 20K miles one way. The 12.5K seats are quite scarce on peak routes in peak periods, so the "availability" you're seeing on Alaska's website is most likely all at the 20K level.

AA won't book SAAver awards on AS flights unless the AS inventory is open at the lower level, since AA prices its domestic SAAver awards also at 12.5K miles.

A second major problem is that the (huge) majority of AS flights to ANC are via SEA, and getting space to/from SEA during cruise season on AA metal is VERY hard due to demand just to get to SEA.

Use the AS website to find seats at 12.5K, trying various AS gateways (SEA, SFO, LAX) and then see if you can put together connections out of ORD on AA metal. You may need to phone for the booking, as the website may balk at things like second-day connections, itineraries with more than two plane changes, etc. Hard work, but you can make it happen.

Also look for first class one way awards, including US metal from PHX. It might be in greater supply, even though US' first class product is pretty miserable compared to AS'.