Upgraded to 5D Mk III recently, since I have really good vision and shoot and focus manually, I have no use for auto-focus points or anything else other than the bottom row of info. I've managed to get all of the AF stuff turned off as well as grids, horizontal level, etc, but now, seemingly out of nowhere I have a dashed circle that just won't go away and I feel like I've searched every setting to try and get rid of it. I just want a clean viewfinder with nothing in it.
The "dashed circle" you refer to is, according to page 23 of the manual (February 2013 edition), the "Spot metering circle". (However, as this circle certainly covers much more than the 1.5% of the viewfinder the spot-meter covers, I see it as being more indicative of the 6.2% coverage of "Partial metering" — see pages 169 and 170 of the manual.)
If you turn the camera off, you'll notice this "Spot metering circle" remains, which tells me the circle must be physically etched on to the focusing screen. So, unless I'm mistaken, there is no way to remove of it, short of replacing the focusing screen.
Page 379 of the manual states the focusing screen is fixed. But, I understand from a colleague, that there are custom-made screens available for the 5D MKIII, and they are relatively easy to replace. You may be able to get a screen devoid of any markings that would suit your needs. However, as I have no direct experience of this though, I can't advise you further.
There are several Canon focusing screens available for different purposes. Take a look here. However, the one you may find useful (depending on the kind of lenses you are using) would be the Canon Super Precision Matte Eg-S - I understand it fits the 5D MkIII but you would need to double check that. Bear in mind, it works best with lenses F/1.8 to 2.8 and is supposed to help manual focusing