Option 1 - Build your own mount
The only way I could see getting either a new stand or a VESA mount is having a custom VESA mount built for this unit.
It's actually not too difficult to build the mount, you just need a flat piece of aluminum or stainless thick enough to attach to the mounting plate of the hinge (area circled) in pic below and long enough that comes out the back of the iMac and either welded or screwed onto a flat plate with the proper VESA mounting holes so you could attach any arm or 3rd party stand.
Making the bracket wouldn't be all that difficult. Any welding shop or machine shop could fabricate it for you. All you really needs is an "L" or "T" shaped bracket (instead of the articulating head in the pic below) for the VESA mounting holes. But you would want the mount to come out of the back of the case in a similar fashion.
Normally, I would recommend this product because it's elegant and German made (German engineering is top rate), but after researching their site, they don't make anything for iMacs after 2011.
The toughest part of this custom build would actually be the complete teardown of the iMac to install your new mounting bracket.
So, it's not impossible, it's just a very involved process.
Option 2 - An Ikea Hack
bmike got me thinking... How to do this cleanly, but very inexpensively...
You could get a shelf from Ikea like the EKBY JÄRPEN and mount it to the wall at a height below your desk that lowers the screen to your comfortable viewing height. Sort of like in the picture below. It's hard to see, but the iMac is sitting on a support on the lower shelf (lighting is horrible)