Could spray some WD-40 or carb cleaner around the bottom of the pan at the crank to see if there is any change in rpms (crankshaft seal). I'm more inclined to think it's use issues rather than mechanicals (cold water running) -- also think it would probably run worse if reed valves were the issue, particularly at idle. But that's a guess.
You are getting some nastiness at the plugs, and I think that kind of fouling is likely due to cold water use. If you run in fresh water, it's not too bad to pull off the cylinder head cover to inspect the condition for fouling -- will guess you probably have a good amount of goop or carbon build-up in the cover. You might be able to clean some of that up. If you replaced the t.stat, you can probably reuse gaskets. (If you go back in, I would replace the pressure release spring just in case. Also, check the t.stat seal -- if the slotted kind, the flange is inserted in the slot.) You could try a decarb. I don't run the stuff in my tank, as I think ongoing use creates issues, but that's an opinion.
Your plugs don't look like L78Vs, based on the length of the side electrodes -- believe the L78s were used(?). A fresh set of plugs might help (.030 gap).