Bookwithmatrix and GF use the same API to bring up the flights on aa.com. It really doesn't matter which one you use. The Matrix/GF bugs with multi-city searches and married segment bucket availability are well documented and can easily be demonstrated with an EF account. What are the specific flights you are looking at? I'm seeing Matrix/GF quote G fares on flights where EF clearly shows there is only L bucket availability on the married segments. This is not something you can simply override. It's absolutely a bug in the Matrix/GF search code. Again, if you simply search based on origin and destination and use the "AA AA AA" advanced routing codes, Matrix will only quote flight combinations where there is actual married segment bucket availability. The reality is you will not likely be able to get the particular routing you want at the cheapest price point.