If you're mounting the solenoid outside its protective box, put it somewhere up behind the support strut in the middle, here's a pic from the "Show the temp in your dash" thread:
The support strut is lower centre of the pic, that pic was taken looking straight down standing in front of the vehicle. That's as long as the cables reach that far! Whatever you do with them, make sure that fluids can drain out of the area so that if it's submerged, it can dry off fairly quickly.
I haven't seen any Anderson-type plugs rated at over 75A (I think). Anderson plugs are rated at about 50A so running 400A through them is likely to cause a fire.
If you're worried about losing the key, just insert the key in the switch and for extra safety, drill a small hole through the key and make a safety line - like a dog's leash - that joins from the mounting holes of the switch body to the small hole through the key. The worst that can happen is the key drops out and dangles around beside the battery.
The objective with the switch is to stop someone from activating your winch without you wanting them to. I have had several people warn me about my winch. Apparently the gag is to release the clutch, pull out the hook about 8 metres or so, run the cable up and over the roof and attach it to your towbar, then engage the clutch and fire off the winch, retreating to a safe distance to watch as the car bends and breaks in your driveway.
I'm not sure if I could ever claim that on insurance, mostly because I doubt that anyone in the insurance company could stop laughing long enough to sign a cheque.