i7 4790K overheating, not the cooler

How do you know its not the H55i? the 4790k is a hot chip to begin with and those smaller AIO coolers aren't up to the task anyways.

Even for an H55, that is an oddly high temperature for a stock 4790k, and idle on the stock cooler should not be above 15c over ambient.

I am starting to think (barring other more obvious answers) it could be a motherboard power delivery issue.

This is the second time I have heard something like this happen. I believe the last one became a warranty issue and intel wasn't a pain to deal with.
And since you seem to have ruled out cooling issues, it might be worth a call.

You could also temporarily reduce your maximum processor state in the bios and see if that drops your temperatures to make the computer usable.

Have you run CPU-Z to make sure nothing funky is happening with the multiplier in the windows environment?
And have you done any bios updates recently?

Do you have any additional software on your computer that could be set to "maximum" performance? That could be altering the CPU multiplier profile?

Aha found what I remembered:
http://www.tomshardware.com/answers/id-2411226/4790k-overheat.html

Bios temps are not idle temps. In bios, your motherboard slaps all your components across the face with voltage. Your CPU could be 55C in bios, but after idling at the desktop for 15 minutes, could drop to like 3C over ambient. At least, my 4790k does that.

Over-tightening the cooler onto the CPU can also have negative repercussions, either by warping the cooler, warping the socket, and/or warping the motherboard itself. A hair past finger tight is enough, especially on that particular bracket. It's mostly plastic, unlike the newer AIO's with square or hexagonal blocks, and can only be tightened so tight so many times.

I tried the stock intel cooler off my i5 4460 on my 4790k just now, center copper slug version. It got so hot, it wouldn't boot half the time, and just typing this puts the CPU at like 65C. Just because it works great on my locked i5 doesn't mean it'll work on an i7. Their heat outputs are drastically different. Your results don't surprise me.

Another thing to keep in mind is the number of people out there who have seen temps drop by over 20C by delidding their i7's, especially the 4790k, 6700k, and 7700k. It means Intel's manufacturing process doesn't result in ideal contact between CPU die and the thick copper integrated heat spreader that covers said die. Intel is also known to use crap thermal compound in there as well. In fact, I'm considering delidding my own CPU.

For reference temperature-wise, my H100i (240mm rad) has problems keeping temps down when the CPU is under full load, even with two of the best static pressure fans ever on there: good old Gentle Typhoons. I carved the H100i open, replaced that stiff nasty tubing, and added a reservoir because my H100i gargled like a drowning man. What really did the trick was removing the thick gasket-looking jet plate that directs water from the pump on top to the cold plate underneath, drastically improving water flow, and subsequently, load temps dropped... a lot. Let's just say, it used to thermal throttle within 60 seconds of launching P95 v26.6 small fft's, regardless of thread count. Now, with the modified H100i, my max load temps are around 86-88C peak, and average 80-83C when the loop reaches equilibrium. I am, however running my CPU at 44 multiplier at 1.2v, because it's unstable with any less voltage. I have no idea how you get away with 1.1V. Lucky you.

Spring1898 brings up some good points:
Intel isn't a pain to deal with. Unlike the time I tried to RMA an FX CPU because my motherboard burst into flames.

Sorry for the wall of text.

Sound like you may have a solution. Just double check to make sure there isn't something installed like Asus Power4gear, or Samsung performance tuning application etc that could be altering the windows power performance settings. The results you show from CPU-Z sound suspiciously like the case mentioned in the link I posted.

But I would get your PSU tested if you can as well.
Most PC shops have basic equipment to test it, and if they have a haswell chipset they can hook up you might be able to kill 2 birds with one stone.

Here are my two guesses for your increased voltages and multiplier:
1.) XMP can do things like this, because EXTREEEEEEME.
2.) Enhanced turbo. Essentially skips Intel's standard turbo function altogether and says, "Hey, your CPU tops out at 44 multi? Let's just run it at 44 multi all the time!" And the voltage follows suit.

Auto voltages running a 4790k at 1.3V+? Sounds like normal behavior to me. My motherboard tried to run at 1.4V Vcore on auto. Blew my mind as much as it blew all of my CPU coolers.

Have you tried fishing through your bios to make sure things, especially the enhanced turbo, aren't on by default? I know that on my MSI Z97 Gaming5, enhanced turbo is on by default, and needs to be manually disabled. I don't know if Asus handles it differently on a different chipset. Obligatory YMMV.