I have a Conti MK2 2.4 on the back of the hardtail at the moment and while it does clear mud quite well and rolls ok grip is pretty average compared to the likes of the DHR2. They do size up narrower compared to Trail Kings so you’d definitely get away with the 2.2 version and maybe even the 2.4. Can measure mine tonight if you want?
If you fancy trying a DHR2 for size I could send you my old one which I think is still lying in the garage doing nothing. It’s pretty worn and the sidewalls are held together by sealant but at least you’ll know if it fits.