I've been installing car audio as a hobby since the eighties. (Yes, I'm getting old.) The door speakers are not "subwoofers," even in the Mach 460 system. Yes, the Mach system sends frequencies below 300 Hz to them (in parallel? That's interesting), but you'll be lucky if they go below the 60 or 50Hz that's normal for most any standard automotive woofer. In the non-Mach system, the door speaker is being used for the full range of audio. If I recall correctly, it's a 6x8 with a whizzer cone?
If changing out the entire system, you'll likely want to install a a component set with a 6.5" woofer in the door, and a tweeter in the upper pod. A subwoofer in the trunk could then give you extended low end response.
If you're not going to install an amplifier, and won't be using a sub, you can get away with re-using the factory wiring, and install the crossover for the fronts in the door as mentioned above. Then find a set of coaxial 6x8's for the rear. The Alpine R series is a decent midline choice, IMO. Even if you do want a sub, you could still re-use the factory wiring, and use a line-level convertor, or an amp with speaker-level inputs. It's not ideal, but can work if your looking to not tear apart the car.
I have a full system in my '95,and would be happy to post pics and details if it will help.