You should be happy that you HAVE 3 speeds, with the option of a MID range. My CK20 is only Hi/Lo, and there are times I could really use the MID gear. I'm usually able to stay in Hi for moving around my property, but there are definitely times I need to drop it into Lo, just for traveling. I've heard that Kioti will be adding the 3-range Hydro soon for the Compacts, too bad they didn't already for mine

--- My buddy's Kub
B2920 (similar size/class) has the 3-speed, and he is able to stay in MID practically all the time.
I think that what the others have said is accurate: the HI is for flat/downhill travel, or whenever it will work without bogging down

When that happens, shift down.
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As for 4wd/2wd use, I keep mine in 4x4 most of the time. I use mine mostly for Loader work work, and I find that the pros outweigh the cons for my use. With that said, on those less-frequent times when I use it for "long-distance" travel, on dry, "flat-enough" surfaces... I keep it in 2wd. UNLESS I'm grading and I need the traction of 4.
Well, I couldn't tell y'a. I normally wait for the tractor to warm up before moving it, but on this occasion I just needed to run next door quick to help out before we were off somewhere else for the day. I started it, waited a minute or so and then started moving in mid range. When I got off my property and onto the road, I put it in high and that's when I noticed the difference. Maybe to oil wasn't up to temp and that was part of my issue, I'm not sure, but going with your theory, the engine would already been using an injection advance and giving me the most power. I do notice more of a rattly sound when cold, but it quickly goes away after a few minutes. I've always attributed it to being cold.
Yeah, mine is very loud and "noisy" for the first few minutes. Seems to stay that way until it's warm and I jump up the RPM's to over 2000. In comparison, my Mid 90's Shibauru 27hp Diesel (in my Ford mower pictured below)... has a much better/smoother sound right out of the gate. Oddly, it has more of an "Industrial" diesel sound, compared to the smooth running sound my Kioti has once warm (if that makes any sense)