New Kemper owner here!! I love this thing, and can't believe I waited this long!
Anyway---I have one of these that I use to store my UA Ox and I love it. So when I recently grabbed my Kemper, I checked to see it if would fit. It did, so I grabbed another from Sweetwater on their finance promo.
As you can see from the pics below, it fits perfectly. I added a sheet of foam on the bottom to rest the Kemper on (not included), then another piece on top (included with the case) so I can keep the cable in there as well. The foam blocks you see are included with the case as well, and they velcro to the sides. This is a great option at a great price. It's cheaper than a Pelican too