So here's the deal with the factory fan wiring: there are 3 wires as you pointed out. The middle one is ground. The other two are power, 1 is for fan on LO, the other is for fan on HI. The ECU (through the CCRM) energizes one wire when LO is triggered, and then energizes the other (not both) when HI is triggered. So if you are only using 1 wire, then be careful which you use, as you will get only LO or only HI.
I would assume the Mishimoto fan would have two speeds as well, and use all 3 wires...is this not the case?
For reference, I am using an aftermarket setup as well, except I have two fans. One fan will come on when LO, and both will come on when HI, using relays and a diode.
Edit: I have a diagram of how I'm going to do this somewhere...
Edit edit: Okay, found an old image. But it's not quite what I am doing:
The only change I have made is that where it says "New Relay" I am not running a relay anymore. Instead, I have a heavy duty diode there instead. When the LO fan is on, it will prevent the current flow from reaching the 2nd fan. When HI is triggered, current will flow to both fans. Hope this helps!
Edit edit edit: Oh, by the way, that's why the fan HI override switch works, because the PCM controls the relays in the CCRM via switching ground. By artificially putting ground in the HI fan input (via a switch) you can force the HI fan on regardless of what the PCM is calling for...