I know I'm reviving an old thread here, but just wanted to chime in and say that you don't need to do anything to put in an 27f. It fits the stock battery tray on a 4th gen without any modifications whatsoever.

I see no reason why you'd want to put in a group 34, its smaller than both the 27f and the 24f. And costs the same amount as the 24f. I have the exact powerx2 27f battery you linked above and its worked wonderfully.

Regarding the dual-battery debate, I'd recommend against using your starting battery for running a fridge unless you have a reliable way to jump your car. Keep your fridge on the lowest battery protection setting. Even on the lowest setting for most fridges, it will bring you into risky territory for your car not starting in the morning by the time it kills the fridge. If you want something simple, look into an ecoflow or similar power bank. Expensive but less expensive than a dual-battery setup and you will probably find a ton of use for it other than running your cooler. Plus you can take your cooler out of the car and bring it anywhere.

Also have to consider that dual battery adds a ton of weight, and if you're using an AGM battery, you are only getting 1/2 of the advertised AH in usable power. 100AH AGM battery= only 50AH of usable power. If you want a bigger battery built-into your vehicle, get a LifePo4 and a dc-dc charger. Way less weight, WAY longer-lasting battery, and nowadays they are cheaper. You can discharge them pretty much 100% so you actually get the advertised AH in usable energy.