Alright, so I have replaced all the carburetor gaskets (including the spacer) and it still runs the same. I didn't replace the carb, but I soaked it in some B-12 Chemtool and it seemed to clear out a lot of junk. Now, the only problem seems to be with the governor.
I tried adjusting it, but it doesn't seem to have much movement on its shaft. Every time I start it, it just starts revving insanely high (it sounds like it's about to shoot the piston right out). I tried moving the idle down some with the governor, but nothing happened.
How can I adjust this governor? Like I said, this mower is a bit of a pain with all the arms, springs, and linkages. Way too complicated for a lawnmower.
You can test it by pushing the gov arm counterclockwise If you can achieve stable RPM by doing so, than adjust your governor by loosing the bolt at the base of the arm and rotating it to the left. However, if the engine continues to surge - the carburetor or the valve clearance may still be the problem.
I tried turning it down a little (counterclockwise), and it's pulsing again. I had tightened the lower spring on the governor arm before, and when I ran it I was able to turn down the throttle a bit and it stayed running. However when the engine speed slowed down to almost normal, it was pulsing again. I bent the spring back to normal and it started doing what it was doing before (idling slowly, pulsing).
I went ahead and ordered a new carburetor, I'll post back if that solves the problem.