I was thinking of this a while back. My biggest problem is lifting the battery in and out of the box as well as finding the correct size battery.

Making it so carpet wouldn't have to be removed and easier to remove and service the battery is the key. Not relocating it.

I was going to make a padded carpeted lid that is actually a larger portion of the passenger floor. Then all I had to do was lift it up without taking anything apart. It would just sit in place with maybe a 1/2 turn lock latch on two corners. I would piano hinge the other end. You could make it flip towards the firewall....towards the seat....towards the hump.....or have two doors that open in the middle with one flipping up towards the seat and the other towards the firewall.

The same idea as the spare tire wheel well in a newer car, just sturdier.