The whole governor and fuel injection pump assembly can be removed together by simply disconnecting all linkages, and oil pressure lines and unbolting it from the accessory drive housing. The shaft connection has an offset tang, so it will only mate back up one way. If you want, you can time the engine up to TDC of compression stroke by looking at the flywheel marks and the valves. Note that there may be markings on the flywheel for both 4 cylinder and 6 cylinder engines, so you may find 4 marks around the flywheel. There should only be one marked 1-4.
Removing the governor from the injection pump housing and rack assembly requires disassembly of the governor piece by piece. If you think there may be problems with the governor, I would just send the whole thing to CAT or a competent mechanic.
One question for you, is the tractor a direct electric start or is it pony motor start? I'm wondering if you have a hand pump on the fuel system that would have come with the direct start setup. Those pumps are a trouble spot to let air into the fuel system and there are other places that may have connections loose enough to let air in, but not actually drip fuel out when sitting. We had an awful time getting our 12E grader primed up after an overhaul until we pressurized the fuel tank by clamping a piece of innertube over the tank opening and inflating it until it bulges out tight. We ended up finding some loose connections on the suction side of the fuel system. Seems like the ferrules were simply loose on the tubing from many years of vibration. Also ended up resealing the transfer pump. If you can get it to prime up with pressure on the tank, but it looses prime when you release the pressure, you have some air leaks somewhere.