You have check that it is actually running on both cylinders?

Walt Conner

I did not see anywhere in your post where you have checked for a clogged vent in the fuel tank cap.
Your symptoms are consistent with a clogged fuel cap. Especially so considering that you get the same results even after "rebuilding carb" and "swapping carbs".
To test this, you can loosen or remove the fuel tank cap when the engine falters and if the engine responds by clearing up..............you have reached Nirvana.
DO NOT USE ether based "starter fluid" to kick an air cooled OPE engine. Use ony spray carburetor cleaner, it's much kinder and gentler to the engine.

Well, in a hurry and missed the part about the "test tank" results. Shucks darn it!!!
Oh, you should never run the engine with any of the shrouding off. Without all the shrouding, there is no cooling air flowing over the cylinder and head.
Be careful, this is a very good way to gall pistons and/or damage the heads.

Walt, it is definiotely running on 2 cylinders.

Mownie was on target. It dd seem like it was fuel starvation and sure enough. I pulled the fuel tank and the line was kinked at the outlet and had trash in it and a split at the nipple. No idea why the other tank failed the hot running. Ran all new hoses and the fuel pump now throws fuel across the shop when you crank it! Good tip on the shroud. I never considered that. I shot both heads with the laser thermometer and they were appx 190 deg on the right and about 10 deg cooler on the left. I went back to the original carb setup, the shroud won't fit the air inlet on the ebay carb and I did not feel like buying a female torx bit to swap the air box portion out.

Cut a bunch of grass with it, we have about an acre that is yard. It runs great til I get into the heavy stuff and then loads down and runs rich. You can see the black smoke coming from the exhaust. Clears up slowly when out of the heavy stuff. Carb related? Governor? What is the small can on the bottom of the carb for? It has a 2 wire connector plugged into it.

I'll do some searching on the drive belt dragging. I have new factory belts in the shop waiting to install. I think it has inch belts installed right now.

Happy 4th to everyone and lots of gratitude to those actively serving in our armed forces as well as y'all retired GIs.

I probably should of mentioned it has new spark plugs and a recently new air filter. Oil is fair but getting changed tomorrow.

The small "can" on the bottom of the carb bowl is called the "Anti-afterfire solenoid" (aka "fuel solenoid")
Its sole purpose is to prevent, or minimize, the bang or kapow that can occur when shutting down a hot engine.
Black smoke under a load! You are not burning high octane gas are you? The higher the octane rating, the slower the fuel burns in a given engine at a specific compression ratio. In this engine, that means some of the fuel charge will not burn in the combustion chamber and ends up being expelled through the exhaust.
Other things that might cause black smoke to appear would be insufficient air supply, or a too large main jet orifice size. You state that the air filter is new, so that should not be a reason for lack of air. But if the air filter box is supplied from a duct or hose, check that for some type of obstruction.
Burning fuel that is old will also produce black smoke and low power.
What is the color of the spark plugs?

Reg unleaded fuel and it is pump fresh. All airbox and carb components were cleaned thoroughly before reassembly.

Update - Changed the oil and Wix filter, was in stock at O'Reillys for $11.00. I changed all the fuel lines out with new high quality fuel hose and darned if it did not start kinking again right where it makes a 90 degree bend where it comes off the bottom of the tank. Butts against the frame work. I got some tightly coiled spring that fits very snugly on the hose and installed it over the bend, and a new fuel filter so that takes care of that.

Ran it again for 15 minutes and almost right away it starts running rough and trying to cut out when in the tall grass and out of it but worse under load. I could feel vibration thru the steering wheel. Occasionally it would clear up. On my motorcycle forum we do what is called plug chops. Drive it til it starts running rough, kill the engine and pull the sparkies. They were both very carbon fouled. I did not notice any black smoke this go round though. Walt, I am liking your idea of running on one cylinder when it starts running badly. The reason I am thinking so is I grabbed the laser thermometer right after pulling the plugs and shot both cylinder heads on the inside of the vee. Left side is 210 deg, right side is 150 deg. This is a dead giveaway that the right cylinder is not firing but why is still arguable. I am convinced the right cylinder is losing fire at times. Overheating coil? I stuck the plugs in the wires and grounded the threads while cranking and got spark on both sides. ??? Back to the carb again? I guess I could swap the 2 coils around and see if the cold head switches sides. What do y'all think.

My guess (and it's only a guess) is a funky ignition module. It sure seems like you've thoroughly gone through the fuel system. Many "carb-related" problems I've tried to troubleshoot ended up being ignition problems when all was said and done!

one other simple thing to chk - you said the engine was like 12 yrs old.. might be a good idea to pull the cooling shroud sheet metal off, clean the fins and chk condition of revealed wiring. Dirty fins could be causing one/both cyls to run hot... and setting up the poor engine performance.

Igniter? Does this engine have one? I'd have no problem throwing on a new one just to see if it clears up my problem.

I removed the sheet metal shrouds and they were not clogged up with debris but the #2 (left) cylinder head was caked up with old oil/dirt that appears to have come from an old valve cover leak. Cleaned it all up and the leak is not coming back so it was fixed last time it was in the shop apparently.

I did see that when I was shooting the temps on the head it is critical that I shoot it at the et same spot on both heads. With the shrouds off they are both running at the same temp so i am abandoning the idea that I have an intermittent dead cylinder. When it starts running rough, kicking off the clutch drive solenoid to the blades clears up the engine right away. Hmmm?

I am opening a different thread for now as I am going to fix my drive belt issue. I will revisit this thread later.

You are right about needing to shoot the exact same spot on each head to get an accurate comparison of temperature.
The area of head associated with intake port/valve will be much cooler than the exhaust side of the head.

OK, I'll ask the question again because I can't find where you have given a direct answer to it.
Have you checked the vent hole in the fuel tank cap to see if it is clogged?

Yes, the cap is spotless and the hole in the top center of it is clear.

OK, had to be sure, not badgering you.
Lets try a different tack just to be sure that this condition is really related to the physical load of driving the deck, or if there is possibly an electrical fault that could be robbing the engine of power.
While you are working on your belts issue, it would be very convenient for you to REMOVE the PRIMARY deck belt from the PTO clutch. With the primary deck belt removed, run the engine and engage the PTO switch. If the engine falters and loses power.........you know it is not due to the deck loading the engine. If the engine begins running badly after the beltless PTO is engaged, check the wiring that serves the PTO clutch for a bare spot worn in the insulation. Usually, a bare spot in this circuit will cause a fuse to blow, but if it is a spot that is not completely grounding out, but instead making a sort of "vibration contact" to ground, it might be causing the fuel solenoid to open and close rapidly as the voltage goes up and down.