We don't have any king comforters, rather my wife and I use separate comforters on a king bed, which is better for us anyway because we have different warmness preferences.

Another suggestion in this forum for the comforter dilemma has been to enclose it in a duvet cover so the comforter itself needs less frequent washing, to be accomplished at a laundromat or cleaner. That isn't the route we take, rather we wash the comforters themselves, every couple of weeks.

I suggest bringing your comforter to a Miele Experience Center or other place with a Little Giant on display, so you can see if it fits. I've found that any comforter which fits into the drum, even snugly, will get wetted and washed. I use Cottons Universal program with Water Plus and Intensive (lengthens the program so there's more time to wet it down), and I have water level raised by 35mm in supervisor level settings. The Pillows program is another possibility, though I prefer Cottons Universal for its intermediate spins which improve rinsing.

All that said, I also have a 3 cu ft Miele W4840 washer. I wash my wife's thick full comforters in there, since I don't like hearing them squeak against the Little Giant's door, and the 40C max temperature of the W4840's Comforters program is adequate for them. I wash my white "blanket-weight" full comforters in the Little Giant as described above, at 60C.