You may find better answers in the Mazda area, but here's what I have to offer:
You need to be able to determine whether the engine and transmission are each operating properly, independent of one another. This means you need to find out whether the engine is delivering normal power, whether the transmission is slipping, and whether the torque converter clutch engages and stays engaged or is slipping. If you cannot feel these things and do not have the tools necessary to monitor them, you'll need to take it somewhere qualified to do a proper diagnosis.