Yikes! That is different.
OK - like I mentioned I'm not an expert in this, I've soldered patch cords before but this was the first time I've gotten this 'dirty' when it comes to car audio. I was lucky plan 'b' worked... I suggest you should have a plan 'b'... I even had a plan 'c'.
What genphreak suggests about getting an old style amp is your best plan 'a' I think - it's a lot less work doing the bypass in Derek A's pics, your plugs are compatible plus you would have your amp as a backup.
That said, I can help you a bit to identify the components if you want to try a complete gutting like I did. The coil inductors are easy - those are the low pass filters (ie they block high frequencies) so almost without a doubt 'W03' is for the front low speaker, 'W02' for the rear low speaker and 'W01' will be combined with a high pass filter (capacitor) for the front mid (dash).
The capacitors could be difficult. Sometimes they are combined to make a different xover point, so it's not certain you are only looking for 3 of them. There will be one filter for the rear tweeter, one shared between the front mid and tweeter, and one extra for just the front tweeter. It's just they could be in pairs or worse so make sure you follow all the circuitry. Use this diagram and work backwards from the plug.
*- The circuits should trace through the capacitors/coils and meet up at the pin connectors to the amp section. This is the amp output, each row is probably for a separate channel ie LF, RL, LR, RR. In each row of pins there should also be a pair of pins for the head unit output/ amp input and a pair for the speaker ground to the head also. This is normally where you would solder the hu output. It might be easier to work with if you remove the amp section. Follow me?
Interesting and nice fix, so you blew your rear speakers too! What kind of glue did you use?