Since you have all the other sizesā¦a 36er is going to make the most unusual ride, other than that I suppose a guni is the next step 
I love my 29", it has been my go to wheel for a couple years, never lets me down, only seems small when Iāve been riding the 36er a lot. I donāt know that anything can really make a unicycle ride less like a unicycle; i.e. comfortable like a bike, but a fat tire can make a big difference in terms of ride quality and āforgivabilityā
If you get a chance to ride a fat tire like the Larry, the first thing you would notice is that it rolls over everything and is not ādistractedā by terrain, so it is more stable and more comfortable to ride. The downside of the fat tires is that 4" of rubber is heavy and has a tendency to go straight and it can be a lot of tire to manage at low and high speeds, so not the greatest tech tire. But to be fair, the fat tire craze developed out of snow/sand riding, so they are not supposed to turn quickly or go fast.
The Knard 29 x 3 is going to be light and narrow for a fat tire, 850gm vs 1200+ gm for the lightest 4" tires, so it is not a true fat, but it is enough extra that it could make a positive difference. The casing is pliable and resilient, Surly knows what they are doing, so I wouldnāt worry so much about cutting the tire on rock. Think of the Knard as a super fat and more durable version of the Racing Ralph.
In terms of traction, no tread really matters when it gets slimey, so really when we talk about traction we are looking at dry traction and edging on semi firm conditions. The Knard is not going to be a carver, it has a rounded profile and a soft casing, so completely different from a Hans Dampf. Dry traction is going to be great, the tire will conform to hard surfaces and friction well, just like the 4" tires. In terms of speed, the tread will be faster than chevron treads, so easier riding that requires less effort. I expect it will also have less autostear due to being narrower and lacking chevron knobbies.
For me, the Knard is going to be my distance rider over varied terrain, cushy and stable to take the edge off the ride and let me relax more. It will also be my snow and mud rider when I donāt need a super fat tire. What the Knard wonāt be is a fast DH carver, for that Iāll hold onto my Hans Dampf. Depending on how it rides, I may build up a super light wheel set for the Knard using a P35 and a 32 hole Oregon hub, but first I gotta see how it spreads out on the Dominator 2 rim.
Josh at UDC USA rode a Knard 29 x 3 for a couple month, then sent it to Roger at UDC UK for testing and specing the Oracle 29 frame. Before riding the Knard Josh rode a Gazz 3", then more recently a Larry and a Nate, but after riding the Knard he said it would be his go to muni tire. I know Josh, I know what he likes and how he rides, if he liked the Knard that much, itās going to be a very good tire. I have a Knard on order, Oregon 29 wheel is already built, only four weeks until it arrivesā¦a late Christmas for me 
You have a lot of unis, so you pretty much know what you like. If youāre looking for improvements on the 29", then a wider spaced hub and a fatter tire are going to be the biggest changes you can make outside of adding a Schlumpf.
As for the 36er, pretty much everyone needs a 36er, and thatās all Iām gonna say about that 
That picture of the muddy road, is that what you ride? Yuck! That is a mess, more like a bathtub of slime than a proper double track, you all need to work on drainage!!
If I was heading out for a ride on that road, Iād take a fat tire because it would motor through the mud and it wouldnāt care about holes and unseen irregular surfaces, but all that weight would be tiring, so for a longer ride on a muddy road Iād go with the Knard or a 36er if I could find a line that was not taking me through potholes. I think you would trash a Schlumpf riding that kind of mud and water all the time, esp. If you are already trashing regular sealed bearings, but there are others who would tell you to go for it.