This may not be a problem with the portal, but rather AA policy. I sometimes finds that the lowest restricted first class fare buckets are only available on aa.com, and not on agency sites.
I am able to replicate one fare through Spirit Incentives [the one that TYP wants $1,200] and it is actually $796 all in with the 15% discount.
The other two [Business class, so can't book through Spirit] I was able to get the same price on Orbitz.
So, in that case, the TYP portal should be able to give me the fare I want?