Crank:
*David talked about polishing his crank until it was smooth for less air restriction..... that's one of those things carried over from a car application. It isn't going to make that much difference at 3800 RPM. Skip it. Just make sure the crank is in good shape.
Head:
*Get a head with the spark plug over the exhaust valve. The 122 didn't have it there. They changed it later. Those heads seem to get a better burn. You will also have to change out the upper engine tin that covers the head with the correct one. You may have to drill holes in it for the fuel tank mount. It's not fussy.
*Bead blast it. Make sure it's clean. Plane it on a sheet of glass, or if you wish, take .040" off of it and raise the compression a bit. I don't, or haven't yet, and I think my motors are fine with the stock compression. You're just plowing, not racing or pulling.
*Do, index the spark plug. Do make sure that the plug threads are good. If they are not, install a repair insert. Make sure that it is flush where the plug seals. I've seen a lot of heads that have been damaged around the plug hole and it won't seal up good. There are a lot of ways you can mill it flat again. Use good judgement on how to do it. A mill is best.
Cam:
*This one is fun. You can run the stock cam and it will be fine. If you have the cash, and want a really good cam, check out Zach Kerbers
Gov 1 and
Gov 2 cams. He has a Gov 3, but you have to do some more changes to the engine to use those. The Gov 1 and 2 both work with the stock lifters. I have yet to use one, but I plan to on a personal build. I know guys who have used them, and report good results. Some people use them alone as an "upgrade" but I think you get a lot more out of the mods already mentioned when used with that cam. Don't think you need to use them.... I just mention them because they are the most affordable upgrade you can do with the cam and not change anything else. Another guy and I (Don Vogt) have discussed them at length, and agree they are a good build, but as I have not used one I can't verify how much more difference it will make. As I stated, I plan to use one in the future, I just have yet to want to spend the extra money on one as I've been very happy with the other mods.
Carb:
*This one is tricky. You will very likely not quite get enough fuel with the other mods made. If you use the Kerber cam, I can about guarantee you won't. I'd put on a freshly rebuilt carb and test run/tune it. If you can't get enough fuel, pull it off, tear it down and drill out the main jet with the next size bit (use a good drill bit set that goes up in small increments). If you have to screw out the main jet needle more than 2.5-3 turns, you need to drill the jet. DO NOT go to a bigger carb (#30). You want the #27 carb.
Timing:
You can likely run the stock timing, but I would play with it. Set it to stock then move it around and see how it acts. Just a note, too far advanced will make it really hard to start. Find the sweet spot. Don't be afraid to move it around. You may or may not be able to tune it by ear. If you have a really good timing light, you can check the exact timing by using the advance on the light to see where it is. I do, then I note it so that I can reset it there if need be. You can also just measure the point gap and record it once you find the timing you need. If you are running a stock cam, it may or may not need something other than stock. The stock camshafts timing was all over the place. Not very uniformly manufactured, so setting the timing to a custom spot isn't very unusual at all.
Well...... that's a lot of info, and you are a long way away from that build. So, process that, ask questions and have fun! I think you will find the K series Kohler to be a pretty impressive engine. If you think all this was cool, you ought to see what can be done with them for garden tractor pulling!

I don't normally take time to be this in depth as it just flies over most guys heads. Hope you caught a lot of that. I prefer just to build a motor and get paid. Maybe you can process it and end up with a good build.
Jeff in PA is the da'man on parts. DO holler at him for driveline needs, or any other machine work you might need. He won't BS you. If he says he can do it, he can. While on the subject, he makes a really nice Brinly adapter. Much nicer than what you have. Not knocking your custom hitch there...... but I'd find an IH hitch and Brinly adapter. There are some things yours is lacking that the correct hitch isn't. Plus, it's kind of big and out there.....
I'll make another post on the clutch.