Dave,
A little history of this tractor would help. Since you asked me for side panels, I assume that you bought this tractor used. Loose intake bolts tell me someone was inside this engine looking for a problem.
I believe Chuck is correct. This Kawasaki engine has a well known problem with leaking head gaskets on the left side. I have bought a couple with that problem cheap because the owner did not want the repair expense.
I am pretty sure we can rule out an ignition problem with the wet condition of the left cylinder. Does wet mean like water or fuel? Fuel would evaporate much quicker than water/antifreeze.
DO you know if this engine has a plastic or steel camgear? Does the engine have any other telltale signs of having been disassembled? Gasket sealer etc. Did you check the compression with the engine warm or cold? I would have expected the left to be a little low on compression.
I rebuilt a FD620D that would run great until it was warm and under a load it and would just completely die. It did not sputter, it was like the ignition was turned off. I went through everything electrical you did and more. Finally I replaced the carb and it ran great. I cleaned the old carb 6-7 times, but there was something that caused the problem. I do not spend much time on WHY questions once something is fixed. I thought I was pretty good at diagnosing engine problems until I ran into this engine.
George of Buford