Don't know layout of rooms, a quick sketch would be nice. Any way to run drain from mud room outside and tie into main farther down stream?
Raise floor in mud room only, ( don't forget, you need a trap in that line) making for less headroom but maybe acceptable in mud room, run drain to main in chase disguised as or hidden in cabinets or built in bench along a wall, or in wider wall.
Low slope with mud is not good idea. Would take lots of water at fast rate to carry away solids and mud could still settle where it enters larger pipe.
A settling or holding tank arrangement might work. Similar to what are used in basement toilets. When tank reaches certain level automatic pump and additional sediment carrying water kicks in.
If line to gravel is far enough from house, has large enough dispersal area, used only from mud room, you may get away with it. Don't know what local code may say about it
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