I have a Nutmeg too!!! She doesn’t kick her litter out but our Arthur used to. The first thing we tried was just simply using less litter and while this worked for litter flinging it did little for the box odor. We completely change the box every other day and freshen it up on the other days by removing the bulk of the favorite pee spot and putting fresh litter in. Second thing we tried was a digging box which was great as Arthur jumped in and played and dug to his hearts content, it quite quickly turned into just another litter box that I had to clean and the sand did nothing to help the smell. Third thing we did was buy a new litter box with higher sides. Even on the days he is feeling diggy the sides keep it contained.
You could also try putting the litter box in a cardboard box with an open top and one open side for entrance and exit. That was what I was going to try next.
I did notice that when we made the digging pool (it was litterally a toddler pool with sand in it) that when Arthur would dig, the force in which the sand would hit the side of the pool was much higher. Not sure if he was just very serious about his digging or he was working out his feelings. Either way, we could always hear when Arthur was in the pool.
Hope this helps.
Chrystie