Hunting and hard starting are more typical of carb problems than a bad plug. A bad plug would make for hard starting (or no starting), to be sure, but once running should not cause hunting. You might check that the choke linkage is working properly and the governor linkages are not gummed up, but there's a good chance that the carb itself needs cleaning or replacement. (Also check that the altitude setting is correct for your location.)
These engines are pretty standard small air-cooled engines, and basic troubleshooting isn't different than for e.g. a lawn mower engine.
Exhaust getting into the RV is a serious problem, possibly caused by a faulty muffler/exhaust pipe, and possibly by an improper installation, a silly positioning of a window or something, or trouble with sealing the motorhome. It should not take a rocket scientist to track down what's happening there. Correct that as soon as practical. A GenTuri (or homemade equivalent) may be an excellent idea even if you find something that needs fixing to get the exhaust fumes up above the RV.
My generator generally hunts for the first minute or two if it hasn't been run recently due to the fuel line having a couple air bubbles in it. Many of the 4KY variants can be primed by holding the control switch in the off position before starting to avoid this, but unfortunately not mine. This just runs the fuel pump without cranking the engine; it may take something like 20 or 30 seconds to fully prime. Generally you can hear a change in the pump's noise when it's set to go.