I've spent the past year really diving into AA status, and basically I put my big non-category spending on the AA credit card, but keep my dining & other bonus categories on the CSR.
The best deal out there is getting the AA credit card with the free admirals passes, and booking hotels through the AA portal on that card. For many 2 night $600 hotel stays, you can get 25,000 AA points and 20,000 loyalty points. Basically works out to 50% off on hotels & fast track to Exec Platinum. I'm booking a few weekend getaway trips in Feb to reach EP, and I've spent very little on actual airfare.