FX850V high idle issues

I have a gravely 460 w the kaw fx850v. Mower lost power and quit. Would only run w choke at about 3/4 closed. Replaced fuel lines, fuel filter, pump, fuel solenoid, and now coils. Runs a little better, but the biggest improvement came when I cleaned the surface of the flywheel magnets with emery cloth. I'm guessing the rusted up after I hosed it off. Ive cleaned the carb once, and it runs no different. Any other ideas out there. Mower only has about 185 hrs. Oh and I adjusted the valves. I'm left thinking its a valve issue or maybe a carb issue. At idle engine sounds fine but as I slowly increase throttle, at about 1/2 throttle you can start to hear a sputter... and at high idle it back fires a lot.

If it only runs with the choke 3/4 closed then it is not getting enough fuel.
The carb might need to be cleaned.
The fuel cap might need to be cleaned if it vents through the cap
If it has a charcoal filter tank vent then that needs to be taken off to ensure it is not the problem.
The manifold might need to be tightend up or have gaskets replaced.
There may be a little spigot on the left side of the carb ( for the said same tank vent ) which has a cap on it if the vent is not fitted, these fall off.

Rust on the magnets have no, nadda ,zero, nill ,nein, effect on the engine unless it is thick enough for it to bridge the gap between the coil & the magnets

Thanks for your help. I had already gone through the carb, but decided to give it one last try after checking the intake for leaks. Sure enough there was a small piece of plastic in the pick up tubes coming out of the bowl. Glad I found it, but no so happy about all the parts I bought.

Still cheaper than taking it to a shop.
I get at least 5 customers every year who have replaced better than $ 500 worth of parts when all that was needed was the valve lash adjusting.

Now the important thing is to look at that little piece of flotsum and work out where it came from because it might have some inlaws about to come for a visit.