I will try to get some pictures for you.
I did this mod as one of my very first, so it has room to grow. While I intend to put in the NHRA legal box and kill switch, for now it's still a street car application.
I used a battery tray from AutoZone and bolted that to the right side trunk floor, through the carpet. The battery is held in place with universal hold down j bolts. I used a plexiglass panel to cover the battery to prevent a crowbar incident. The plexiglass is also a great spot to bolt in a fuse or breaker panel and a local disconnecting means.
I ran my positive connection from the engine bay fuse panel to a hidden 300Amp 12v disconnect switch in the jockey box, and from there to the battery. In hindsight, I should have gone to the starter and then to the fuse panel. I am a fool for grounding and bonding so my negative wire goes from the battery to the engine block, with extra grounds locally in the trunk near the battery. I also ran a bond from the engine block to the firewall.
I ran all my cables through the OEM wire tray where possible, penetrated the firewall at an existing gland. From the jockey box to the battery, the POS wire lays under the back seat. I put this section inside a garden hose for added protection. Don't run your wires outside the car, especially beneath the car for obvious reasons.
I was really surprised by the handling difference this made to my car. I upgraded my suspension, steering, wheels and tires after the battery relocation, so I did get a good comparison. The car feels lighter and the front stays well planted without any pushing. It feels safer, more solidly connected to the road in turns.
Incidentally, I did this before I re-geared and added traction lock to the car and it made a big improvement in traction. My car used to do the one wheel peel or with trac assist on, fight with itself trying to launch. Neither was good. Moving the battery allowed me to shut off the trac assist and get both wheels to spin better than previously.
I don't drive my car in snow, but I imagine it would help there as well.
I like to run two batteries in boats and trucks, with the appropriate bat 1, bat 2, both switch. This allows running an inverter without concerns.
It seems like too much added weight for the Cougar to have 2 batteries without obvious benefits. I have taken some weight out of the car with the engine swap, RLCAs, diff housing, etc.