I actually had the non monsoon system in my car, but I replaced everything.
Installed a DDIN headunit using the Metra DIC kit, Ran RCAs back to the trunk for my 4 channel and mono channel amps.
Ran all new wiring from the amps to my speakers and sub.
However, as I said in my post, the monsoon system has an amplifier between the headunit and speakers, so if you plan on bypassing that then you will want to run all new wiring.
From what I have read, people have been getting subpar results from using the monsoon amp with an aftermarket headunit.