What battery specs actually matter?
Reserve (measured in amp hours AH) and C rating (which is a multiple of amp hours).
The specs those JY clowns post have the caveat right next to their ratings of "at 2C" or "at 1C" which means they're mix-matching maximum safe numbers with optimum and intended numbers depending on which makes their marketing hype look best. I could not get honest answers from any of those snake oil salesmen when I was battery shopping so I just bought my own cells from China and went the DIY route.
Anyway if you're planning a 300A alternator it will be trying to charge your batteries with 300A (probably not real world but safe to assume it may). Let's say you pick a 30AH battery with 10C charge rating that means the maximum current you can safely charge with is 10(the C rating) X 30 (the amp hour rating) or 300A. There is a big difference between the absolute maximum you can do before rapid or catastrophic failure and normal intended continuous use that will not dramatically shorten the life expectency of your battery and lead to poor performance.
Same story with discharge rating. Let's say your 10,000W rated amps will attempt to draw 1000A of current, even 100AH of 10C rated cells are working at their straight out max limit (though since AH ratings are at 1C you're not even doing that well) and both voltage and current capacity will drop extremely quickly under load.
In short, if you're coming out the gate trying to pinch pennies on a battery bank you're setting yourself up for failure from the start. If you can't afford a big battery bank you can't afford a 10,000W audio system period full stop.
From there Lincoln Town Car is one of the absolute worst vehicles to try to get sound up out of the trunk in. I did a 1980 towncar many many years ago and the build was costly and very labor intensive and it still wasn't anything special for how much stuff I had into it. I really love Lincolns but I would not consider an audio build in a car like this short of deleting the back seats and doing a B-pillar wall.
It seems like you are in way over your head here, trying to cram 10 pounds of **** into a 5 pound bag using a plastic spork. I would encourage you to go back to the drawing board on this whole project, otherwise what I foresee happening is you spending a lot of money on equipment but not enough to really do it right and winding up with something that is only good for creating the amount of trunk rattling that you could have bought from Best Buy for under a grand.