Hi, Corey,
Sorry for the delay in getting this information posted.
Last question first . . . there's some goofiness because the input to charge the ArkPak is 24 volts DC. Both the AC charger and the optional DC (car) charger output 24 volts. I looked up your charge controller and it (totally as expected) outputs 12 volts. So you can't directly hook the Bruton up to the charging input on the ArkPak. It might be possible to connect somehow to the battery cables so the 12 volts went in that way, but that would be a bit of a kludge.
The optional ArkPak DC-to-DC (12 to 24V) car charger has a female power plug (lighter-type), so the "right" way would be to buy the car charger and then replace the ring terminals on the end of the Brunton's cable with the female lighter receptacle. When using the solar panel, plug the small male cable end of the ArkPak DC charger into the Arkpak and plug the big male lighter end into the female socket you just put on the end of the controller. That should work a treat, as the charging program built into the ArkPak is pretty sophisticated.
The expense of having to buy the DC charger to use your solar controller won't seem so bad if you'll also be connecting the ArkPak charger to an in-car power port to charge the battery, which you'd want to routinely do while driving.
As for the shortcomings raised in the forums . . . I don't understand the most negative of the comments. The case is no great piece of art--it's thin black plastic that fits the innards as tightly as possible. I assume the goal was to make it as small and light as needed for the job, and that's what it is. The cover for the controls seems a bit flimsy because it's made of the same thin black plastic, but the handles are secure and the case is protective enough. The key point is that I'm not sure you'd want to carry, or pay for, anything more elegant.
The ArkPak makes some noise, but it seems to me a close match to a chest-type compressor refrigerator in volume. It's basically cooling fan noise, and about equivalent to what I have on my other inverters, which are expensive Prosine units. I don't know what was with the guy who had the deafening one; mine "whirs," sometimes noticeably, but you'd have to be really sensitive to be bothered by it when awake, and most people could sleep with it close by. (And given that it's portable, if you're a light sleeper, just move it away from your head.)
The smallish modified sine wave inverter is the weakest link of the product, in my opinion, but it's not a bad inverter and it doesn't seem any more prone to causing troubles than any of them. (And, like the case, if the inverter was bigger and heavier, so would the overall package, so it's just a design choice.) Different equipment reacts differently, but most anything you plug in that gets current through a separate charger, like a laptop or tablet should be happy. I don't have an iPhone, so I can't comment directly on that specific issue. I certainly have no problems charging my outdated LG phone off the USB connector.
The ArkPak wasn't designed to be perfect in all ways, but if you look at it as a couple of days of camping electricity in a transportable box, it'll be pretty appealing for certain users.