You will need a factory integration processor DSP such as the JL FIX 82 or FIX 86 or similar like the Rockford 360 that can take speaker level inputs, flatten the factory EQ and time alignment, and output a flat clean signal that you can work with to your amps or other DSP.
You can use one of those PAC LOC units to make hooking up the high level inputs plug and play on most radios (not completely sure about yours) and just not actually use the PAC LOC. this way you don't have to cut any factory wires.
BTW, did Mazda finally address the issue where the songs on an iPod or iPhone start at the same song every time you restart the car and also take forever to load. I own a 2014 Mazda CX-5 Touring and still have the factory radio for now. My brother in law has a Mazda 6 with the Bose system and his has the same issue as mine.