Lowering iMac height
How to (inexpensively) lower the screen height of an iMac 27? (late 2013 if it matters)
I can't damage the computer so torching the stand until it bends to lower the height of the screen is out of the question.
According to Apple: iMac (21.5-inch and 27-inch, Late 2012 and later) computers can be configured to order with a built-in VESA mount adapter when ordering via the Apple Online Store. (...) VESA mount adapter upgrade kits are not available for iMacs with a stand.
Solution 1:
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)
Solution 2:
Inexpensive - no way to modify the Mac. Instead modify the table or change chairs or what the person stands on. Those are all far less expensive to customize.
The expense of opening or modifying the Mac is the self-insurance you need to set aside if you damage and/or break something and have to pay for it to be fixed professionally. Not all open/repairs break something, but these iMac aren't trivially opened due to how thin and delicate they are and how the adhesives to keep it solid need to be carefully managed and replenished each repair.
Solution 3:
I used two options, both based on a vertically adjustable keyboard "tray" (not really a tray, just an adjustable portion of the desk meant for the keyboard):
Option 1) I used 3" length thread stock to extend/raise, rather than lower, my keyboard portion of the desk. Then I simply raised my body to be ergonomic with the keyboard and iMac display - my chair extends tall (for use with a drafting table, for instance). And a footrest because now my feet don't reach flat on the floor.
Option 2) I lowered the keyboard portion of the desk (as is the normal functionality of that piece), placed the iMac on it (now lowered), spun the desk around and sat at the normally "back" side of the desk at normal height with the keyboard on top of the desk. It looks just like the ikea hack pic in this thread, only it is part of the desk rather than a shelf attached to the wall. I got similar effect of these iMac "well" desks from Smartdesks (I do not know what they cost) http://www.smartdesks.com/imac-computer-tables-apple-mac-computer-desks.asp