18 hp Intek OHV Model 31E777 0443 E1 on Craftsman LT1000...Need Help! Thanks

Craftsman LT1000 Riding Mower
Briggs and Stratton 18 hp Intek OHV model 31E777 0443 E1

Problem:  

Briggs and Stratton Intek OHV Single Cylinder 18 hp starts and 
runs very smooth from idle (1800 RPM) up to about half throttle
(around 2300 RPM).  Readings taken from tachometer I installed.  
From approx. 2400 RPM and up, it starts intermittent loud popping
sounds from out of the exhaust with some puffs of black smoke.  
This is much worse when the blades are engaged and cutting 
particularly when I go up any incline or turn swiftly to the right of if
I hit bumps like tree roots while I am cutting the grass.  It
becomes non stop rapid popping (every stroke of engine) when 
cutting on an incline with mower’s left side on the down hill side.
After cutting the grass with this happening (by the way at just 2400
RPM maximum) the spark plug has black soot on it, not totally fouled, 
but if I left it for the next mow, it probably would be.  I have already 
tried many things to fix this, but I am at a loss and I am looking for 
some internet magic to happen.

Here is what all I have done and my observations.  By the way, none
of my efforts have had any effect on the problem:

1.  New Air Filter, Oil Changed, and Oil Filter.
2.  New Armature w/ wire, and spark plug (properly gapped).
3.  RPM gauge installed. Flywheel magnet cleaned off.
4.  Valves adjust to recommended .004 intake .006 exhaust.
5.  New Fuel tank (looked cracked on top), fuel lines, and filter.
6.  New Carburetor and intake manifold gaskets.
7.  Checked Flywheel Key.  Perfect unmoved/intact.
8.  Took off head and removed all carbon deposits.
9.  Inspected and lapped the valves for proper seal.
10.  Cleaned both exhaust and intake passages in head.
11.  Installed new gaskets from head gasket to manifolds.
12.  Gapped and Installed another new spark plug.
13.  Readjust new carburetor idle and speed screws.
14.  Drained carburetor bowl (no water) inspect solenoid (NIKKI Carb)

Thoughts:  For some reason the engine is either getting way
too much fuel dumped in to the piston chamber during the above
mentioned driving conditions, or somehow oil is getting into
the piston chamber under these conditions.  As for the oil
theory, which is how I am leaning, the only route oil could 
get in there after all the work and inspecting I’ve done is 
in through the breather tube.  Piston rings are sealed or it
would smoke and burn oil more consistently, and valve
seals are tight.  Any ideas, assistance, or experience with
these engines and this problem would be greatly appreciated.
I am out of ideas at this point.   Thank you in advance

What is the date code? I wonder if it came from the factory like that or if somebody was mucking with it.

It ran like that for 14 years?

Glad you found the problem and reporting the solution as it can help someone else later.
 
The only time I ever had a problem with one these reed valves was when I was clearing the area of old caked oil but that user had ran the mower with a bad head gasket until it blew so bad that the engine failed to run. Yes had to make sure the reed was aligned properly as it would move upon tightening the retaining screw. Finally just stuck a spacer in there until I got it tightened.

okay I am new at the small engine thing but reading all the post on this problem makes me wonder if it is something else.  from what I am reading is it runs alright with no load ie. it gets up to 3400 rpm's no problem engage the blades it drops to about 2500 rpm's,  put a load on it and it pops black smoke that usually means its running rich to much gas not enough air, or it is still burning fuel on the exhaust stroke.  either way not enough air for a correct fuel to air mixture.  Could it be a governor issue.  Before everybody jumps on me remember I am new at this stuff..  The governor should get the motor back up to speed if under the load, correct? and shouldn't the timing also be advancing a little to compensate for the increase in fuel entering the carb because of the wide open throttle.  Me i would put the idle screw back to factory setting along with the mixture screw, start the motor engage the blades and manually move the governor to see if it moves and it the engine speeds up with no popping.  again be kind new at this.

If after I put another carb on it still no change then I am down to popping open the crankcase inspecting the governor inside and replacing the cam. After that there is nothing left but to get a new motor. So, I plan on trying one more carb, then pulling the engine.