Production is different from the other divisions: there is an continually updated list of approved models. If it's not on the USPSA Approved Production Gun List, which can be found under Match Rules on uspsa.org, it's not legal. Doesn't matter whether the model just meets the letter of requirements for the division.
Manufacturers actually have to submit new models for eval and approval once they reach a total of 2,000 manufactured. The S&W MP Pro just made the list, IIRC. A number of people were waiting...somewhat patiently ...for that announcement.
Come on out to a match and shoot, it doesn't matter where your gun "fits". When you first start there are many things to learn about gun safety, gun handling, where to make a reload, breaking down a stage, and others. Limited would be a great place for you to start. You don't have to worry about reloading very much and you will be shooting a gun that is familiar to you as well as easy to shoot.
Come on out and shoot...I guarantee you won't regret it.