I had some extra time at work and its something I could make with what we have there so I decided to try it out. I did most of the mixing and folding yesterday, 2 turns, then did the last turn and shaping today. I ran into a few snags, such as the dough hook for the mixer disappearing, but in the end I persevered and ended up with some decent kouign amann. I think. I've never had them before, so I have nothing for comparison, but they were pretty good. A little salty to my taste (and the taste of pretty much everyone else who tried them) but not so much as to prevent people from finishing it or in some cases having more. (I had three.) I didn't make all the dough, though, so I'm gonna try again, reducing the salt. (I'm also gonna use some of the dough for croissants. Mmm, love those...)
So right off the bat I ran into issues as I couldn't find the dough hook. No idea what might've happened to it, its never been used since I've been there and I last saw it in a box of parts. Wat. Annoying, but unfortunately not entirely unexpected at this place. No biggie, though, I used the dough blade for the food processor instead. Worked well, although it was slightly too much for the proc volume-wise (made a double batch). Mixed it up good in there for a bit then kneaded by hand for a few minutes. Not as long as it would've gotten in the mixer, but what can you do... Also, we don't have cake flour, so I had to use AP.
heres the dough laid out waiting for the butter block:

I at least had the paddle for the mixer, though, so whipping up the butter block went smoothly:

I'm not actually sure why we even have one, as its not necessary and I've only ever used it for doing things for myself, but luckily we do have a rolling pin, so rolling and folding went smoothly as well. after fold one:

When putting in the butter block, I trimmed the dough a bit for a better fit. Rather than discarding it, I decided to just roll it up and bake it on its own as a roll. It came out slightly dense, but otherwise made a nice dinner-roll.

Next up: shaping. (To be continued in a reply since I'm not sure if theres a limit on the number of images per post here.)