Hi, This is what I use. Seems similar to what you have for your MTB... So far it works fine and helps avoiding to do a mess on the floor and back wheel. First I put the degreasing and run the chain through the "case-brushes" device, then clean whole chain with a cloth, finally grease within the same device and let her "rest" for a night. https://www.louis.eu/artikel/kettenmax-louis-edition-chain-clean-lube-device/10003114
My 70 cents (about 50p) brush arrived recently so I got to work with it. It did a beautiful job of cleaning the chain.