JL1000/1 + 450/4 + W7 - Battery/Wiring

I have a 2000 Ford Contour SVT with a JL Audio 450/4 powering a set of Focal K2P components up front, and some Eclipse 6x9's in the back, with a JL 1000/1 powering one 12" JL W7. I got a Alpine 9835 deck, with a 1 farad cap. Maybe you guys can give me some insight on the problem I am experiencing and the best way to go about fixing it.

 

Currently this is the problem: in addition to lights dimming when bass hits, if I turn up the volume too loud or turn up the sub specifically too loud, my mids and highs will cut out for a few seconds, then come back and do this continually till either the total volume is turned down, or the sub is turned down. Now, one thing I should note is that I only have 4 guage wire running to a fuse block split off to both amps. I know that this is horrible, but the wire was existing from before I got the sub, and didn't know enough about audio to know that I needed to upgrade the wires. I have a JL Audio amp kit with 2 guage wiring ready to upgrade my existing wires.

 

 Additionally I want to get a new battery. Will getting a battery such as this http://www.gotbatteries.com/items.asp?params=search/SLA/1/Odyssey/PC1200 help solve my problems when I upgrade the wiring at the same time? I believe the alternator on the car puts out 135 amps, and I've been told that is enough for even a multi thousand watt system. I don't mind my lights dimming too much as I do the sound cutting out. I'm not sure exactly the reason it does this, so any and all advice is greatly appreciated. I wish I knew about this site a long time ago.

 

-Arjuna