Welcome to Flyertalk and welcome to the BA forum lvA6.

There are essentially two potential impediments here - the restriction of BA's website (and OTA websites) to do more complex bookings. Calling up may help, particularly if you read out the schedule as "BA123 on 1 Feb in D, AA321 on 1 Feb in I" and so on. The second are genuine blocks where ticket times are not allowed to be combined. Tools like ITA matrix may well have this itemised in the verbose rules, but ITA matrix isn't above combining these fares illegally in their searches. I suspect it's to do with minor flag settings not picking up all the restrictions.

Having said that, I'm trying to work out why booking via AA.com would be a problem, it's not something that would inhibit me from booking on them. There are differences with Buy With Confidence, but if that is the reason I would seriously question the logic of making a "maybe" booking.