Glad to hear you got it working. I have never actually used the stock speakers with a different head unit, I replaced my speakers at the same time. My right side front was cutting out as well and I just replaced them with some 6" seperates. I don't think there is another amp behind the dash like hammong said, on mine the amps were part of the 6x9 door speaker.
When wiring regular speakers, there are 6 wires in the door going into the speaker; 2 go up to the tweeters, 2 come in as speaker +- and 2 are power for the builtin amp. I put my crossovers in the door as all the wiring for the tweeter and woofer is in the door. Just leave out the power for the stock amps, run the input into the crossover and the output to the tweeter & woofer. I posted the wire color for all the wires in the door going into the amp, search for a post by me and it should come up, if you can't, message me I will try to find it.
The rear speakers are pretty easy, they don't have any tricky stuff going on. Actually, the stock rears in mine handled power pretty well without distorting. I did replace them with new speakers that match my fronts. I did have a filter in the amp filtering out the bass.
My system is:
Alpine 7939 AI-Net Head
6 disk AI-Net changer
Phoenix Gold M44 (4x40w) powering the 4 speakers
Phoenix Gold M50 (1x200w) powering Sub
MB Quart 218. 03CX Front 6-1/2 separates
MB Quart 215. 03CX Rear 5-1/4 separates
JL center seat cusion 12" sub
I don't know about where to get the door christmas tree things.
Good luck