The inner damper rod is positively located to the perforated cartridge shim at the top using split collets. However, once the collets aren't there, the damper rod slides down into the fork, and is nearly impossible to pull back up without removing the fork tube.
Fortunately, we were alerted to this possibility before anything bad happened, and threaded an M4 screw into the top of the damper rod with a string attached to it to hold it up when the collets were removed. The string makes it easy to tie off to a grip or fairing location should you not have a spare hand to keep pressure on it.
After pushing down on the cartridge shim and removing the collets, you should be able to pull the perforated cartridge shim out. Be careful while you pull it past the bolt head which you have threaded into the damper rod, otherwise the string will be severed and the damper rod will slide down into the fork.
Once the shim is out, you are looking at the top of the fork spring, which is retained by an internal spring clip. This took quite a bit of fiddling on our part to remove, mostly because there was little to grip on. Be careful around the threads, and pull the spring out when the spring clip is removed.
We installed the new fork springs, inserted the spring clip (we used a spark plug wrench to compress the fork springs), and the rest went back together without a problem. Don't forget to tighten the upper triple clamp pinch bolts afterward.
Hopefully this will help anyone looking to install fork springs on their late-model K1100.