Thanks for the photo.

I am unfamiliar with the details of the 2005-up voltage regulators but I know a thing or two about batteries and charging controls and can guess at most of it.

What you call the "box on the negative battery cable" is a current sensor. Its purpose is to measure the current (amps) to and from the battery. It's one of the pieces of the puzzle that the computer has to have in order to accurately determine the ideal output voltage to set the alternator for. Battery temperature and the amount of time since the engine was started being the other important variables.

So here's the scoop. See how you have two wires that both go from the - battery terminal and then through the ring of the current sensor? The large one goes to the engine block somewhere, and the small one goes to the sheet metal of the chassis, usually on the fender or to part of the radiator support structure. If you want to do a big 3 what you want to do is replace those with a single wire going from the battery terminal, through the ring, and to the engine block --- and then attach the existing little wire, the end of it that used to go to the - battery terminal, to the big wire by soldering a running splice, like this:

Engine ground------------+-------O------- (-)battery
.. . . . . . . . . . . . |
.. . . . . . . . . . . . +---- fender/radiator support

Where the "O" is the sensor.

You'll find that without the little wire having to fit under there you can upsize the wire by at least a couple of sizes. Might want to take it to the parts store and test fit it since insulation thickness can vary from one wire type to the next.

You make the running splice by stripping about 1-2" of insulation from the part of the larger cable where the splice will go, then wrapping the (stripped bare) end of the smaller wire around it 3-4 times. Then solder it with good, rosin-core, tin/lead solder, and wrap it with tape. A 300W soldering iron or gun works best but a torch will work too as long as you're careful not to overheat the joint.

The current flow through the sensor with this setup will be the same as what you had with stock so the performance of the charging system will be exactly the same. In essence you want to run all the ground-to-battery connections through the device, but not any other grounds.

ETA: Dots. Ignore the dots in the diagram, they're there so the forum software won't change the spacing