Small Engines (Lawn Mowers, etc.): John Deere 335 running weak with mower on., kawasaki engines, engine rev

Question
I have a John Deere 335 with a Kawasaki V-Twin engine E/No FH601VA09678.  Last year I ran it out of gas.  After I added new gas the mower sounded like it was running on one cylinder for a while, then it returned to normal.  I tried installing a new fuel filter, thinking that maybe dirt got sucked into the filter from the bottom of the tank, that didn't help.  This got progressively worse last summer.  Last fall I changed the oil, oil filter, installed another new fuel filter, new spark plugs, and a new air filter.  Still wasn't running right.  I removed the outlet hose on the fuel pump and verified that fuel was pumping.  At the advise of an answer from another question asked to a different expert here I removed the solenoid on the carb and replaced it with a bolt of the same size, no luck. This spring I cleaned the carb, and installed a carb kit.  This still didn't solve the problem.  My father in law looked at it and discovered that one of the coils was bad, so he installed a used one for me and now the motor runs smooth until you engage the mower.  With the mower running, the engine is smooth, but it sounds like the throttle is only running about 80%.  If the carb is adjusted to the point that the engine rpm is where it should be with the mower on, then the engine wont idle.  I am able to still mow, just very slowly.  Could this be some sort of a governor problem not having the engine rev up enough with the mower on?  Thanks for your help, and sorry for the lengthy question, just trying to give as much info as possible.

Answer
hi brandt

here is web site

http://www.partstree.com/parts/?lc=kawasaki_engines&mh=26,78

yes you could try governor adjustment,try it 1st , it could be  load exceeding power output
as you mention sounded like running on 1 cyl - have you checked  that both exhaust headers are getting hot

have you checked compression from both cylinders ?

have you checked  valve clearance  for both cylinders ?  could be a tight valve clearance

muffler is not restricted is it ?

have you checked for leaking inlet or exhaust valves ?
or leaking inlet manifold header  a leak at one end of inlet header will affect only that cylinder  noth both

what is the plug color of the cylinder thats playing up or had the replacement aramture


have a check and let me know  what you find


cheers paul