I've steered a few people to LG front-loaders and they have all been very happy with them. The WM8100 sports a 5.2 cu.ft. drum, which should fit the bill for your king-sized comforter. A compatible LG dryer can be stacked on top of it. LG's reliability, owner satisfaction, and wash performance/cleaning scores are excellent.
I had a Frigidaire front-loader with a 3.5 cu. ft drum and it held my cheap, lightweight queen-sized comforter (purchased at Target or ShopKo). It was a tight squeeze, though. A king-sized comforter, especially a more expensive one of a heavier weight would not have fit in the machine.
Note: The photo at the link to LG's website shows the 8100 paired with the little "SideKick" mini washer (purchased separately). You would not be able to stack a dryer on top of the 8100 if you choose to add the SideKick. The photo shown below is of the 8100 and its companion dryer on top of it, which I'm assuming is the type of set-up you're looking for. The mega-capacity 8100 sells for around $1200-1400.
One more thing: If your king-size comforter is of a lighter weight, it may fit into a washer with a 4.5 cu. ft. drum, like the new LG3900. I had a Maytag with a 4.5 cu. ft. drum and my queen-size comforter fit in it with room to spare. The LG3900 can be had for $900-1000 dollars. A compatible LG dryer can be stacked on top of it.
The best way to know if the comforter will fit into a particular washer is to bring it with you when you go washer-shopping. It sounds crazy, but I strongly recommend doing that. Then you'll know whether it fits or not before you have the washer installed at home.
Frankly, I think you may like an LG so much that it becomes your daily driver![this post was last edited: 9/27/2019-18:00]
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