^ There we go. Well someone else can help suggest a stout battery for under the hood, they tend to run $200-$300 bucks, but it will help a lot when you've got a 1kW sound system, and the TV's going, especially with the larger alt that you have.
I'd say maybe a single 15" for you then. A lower line would be the Obsidian Audio 15. They can handle 1000w pretty well, although they are conservatively rated at 600w.
Obsidian Car Audio
And as you increase in budget, there's the Skar 15, their line of woofers is well known for handling the low notes very well, which may be even better suited for your musical tastes.
SSA Store - SKAR Audio VVX Sub woofer
Then the SSA ICONs: Known for getting loud and still being clean at higher volume levels:
ICON-15 D2
And the IA Flatlyne, IA's much more SQ oriented woofer, still capable of getting plenty loud

:
Flatlyne-15 D2
These are just a few woofers that could fit the specific application of a single 15", at 1000w. And those are just brief stereotyped descriptions of their abilities. Obvious performance will vary with your enclosure and vehicle. Hopefully some more people will chime in on maybe a single 18" or a pair of 10s or 12s, just depending on how much space you wanna give up.