I read this thread a year ago and I thought "boy with my luck I'd cross thread something trying to get it back together" If that happened I'd have to go and buy a Robur or something as a replacement...
FWIW, my grinder is about a year old and is a Mini-E (type A). I've used Grindz twice a month faithfully (grinding usage = 4-6 lbs. a month).
I re-read this post a few days ago and saw Karl's success and thought why not give it a go myself? So with HB instructions in hand...
As others have said, this turned out to be such an easy task you'll wonder why you ever balked at tearing the grinder down for cleaning before. If this is a 10 minute job, that's only because 9 of those 10 minutes are spent cleaning the burr carriers. Dis-assembly and assembly turned out to be a piece-of-cake.
A few personal observations:
Even though I've used Grindz as stated above, I still had a bunch of stale old coffee packed into the "corners" of the upper and lower carriers; particularly around, along and below the ejector vanes and in the screw recesses.

A stiff nylon bristle brush and my shop vac made quick work of this. (Anyone use a soft metal brush, such as one with brass bristles for cleaning the burrs?)
First time I've had it apart in about a year of ownership and Mazzer had gobs of white grease on the threads and smeared around on the inner collar. Hmmm, Cannonfodder was right about too much goop! This was cleaned up. I didn't re-lube anything.
The thing that intimidated me the most was the thought of trying to get it all re-threaded again while under spring pressure, as I would have to apply downward pressure in the throat while trying to screw everything back together etc. You know, strip the threads and have to buy the aforementioned Robur... At least for me, it turned out to be a non-issue. On my grinder there is enough "slack" in the threading so that I could get the threads started easily without much downward pressure (if any at all) before it then started to tension the springs.

I tried this several times just to be sure it wasn't a fluke and each time it was the same. As Dan said, spin the collar CW (loosening) until you feel the threads drop firmly into place and then reverse direction (CCW) to tighten it up. There is a fairly obvious "click" when the threads drop and engage.
I also spun the collar around to different points to try and get the threading to start at a different position than the collar removal mark that HB suggested but I couldn't find any other spot where the threads would engage. There seemed to be only one point where threading would start (which then always took me back to the original zero point for the burrs- Wow!). So I'll probably skip this collar mark step next time.
Lastly, I made a mental note where the hopper lock screw hole was in the upper carrier throat (even though I've long since removed the screw to facilitate a quick hopper off for cleaning) so I would mount the equidistant upper burr carrier studs in their original position (if this matters).
The only other thing I would throw out is that I've had to take the push button DL "lid" of my type A apart on a couple of occasions as the vibration from the grinder seems to eventually rattle loose the little hex nuts that hold the inner circuit board in place. They then rattle around inside the lid when I grind.

Two Phillips screws out and apart it comes. Even though a rubber O-ring seats the lid halves, it was suprising to me at first how much espresso dust wiggled in there as well-
Cleaning the Mini turned out to be such a simple job that I'll probably skip Grindz in the future and manually clean my grinder every few weeks instead.
Now for the best part- the shots I pulled after this thorough cleaning were some of the best I've had in a while!
Thanks for this thread guys!