Briggs 12.5 hp hot muffler and running uneven

Hello, sorry for my poor English, I am a disabled person from Central Europe and I have a problem with my briggs & stratton engine, I need an advice.
The engine model is 12.5 hp briggs & stratton 286707-0115-01 manufactured in '93, the problem is the muffler is hot, it turns red on the outside and glows orange on the inside after 20 minutes of operation.In addition, the engine runs unevenly, I recorded it on video.This problem existed in the past, but I ignored it because the engine was in bad condition and consumed a lot of oil, and I had no money for repairs. Now I finally decided to do a general overhaul of the engine, list of things that were done in a professional workshop, the cylinder was grinded for the oversize piston + 0.5 mm (0.02") and honed. Resurface Cylinder Head and cylinder for a new head gasket.
I did the rest myself at home, the parts that were replaced: piston with rings, pin, connecting rod, all new gaskets, filters, spark plug.
I also manually lapped the valves with medium-grade paste. There was a lot of carbon deposits on the piston, valves and head, I removed it all. The valves were definitely not tight due to carbon deposits. After lapping, I checked the tightness with 100% alcohol, the intake valve is perfect, the exhaust valve was a bit leaky, due to lack of time I did not fix it, although lapping improved its tightness significantly. I think that the slightly leaky exhaust valve is not the cause of the hot muffler and uneven engine operation because before the renovation the valve was very leaky and the muffler was slightly red, after the renovation the muffler lights up red and orange and the engine works the same.
The gaps on the rings are
compression ring 1 0.35mm (0.014")
compression ring 2 0.45mm (0.018")
oil ring 0.55mm (0.021")
Valve clearances are: intake valve 0.15mm (0.006"), exhaust valve 0.25mm (0.01").
Gap between the coil and the magnet wheel is set to 0.25mm (0.01").
Before the renovation, the engine worked unevenly, smoked a lot, consumed a lot of oil, was getting weaker, and the muffler was sometimes slightly red. After the renovation, the engine is powerful, the exhaust gases are completely clean, without any smoke or smell. Unfortunately, the engine still runs unevenly and the exhaust heats up even more. The engine was very worn and had play in every element. I managed to eliminate all clearances and wrong dimensions in the cylinder, piston, rings, valves, and halved the clearance between the shaft and connecting rod. During the off-season, I plan to renovate the crankshaft to restore the original dimension on the counterweights and connecting rod.
As far as I know, my engine problems may be caused by poor ignition timing or too lean/rich mixture. As for the ignition, everything is original, the ignition advance time cannot be changed in this model. The magnet wheel was in place when I disassembled the engine, and when assembling I certainly installed it correctly and locked it with pin.
As for the carburetor, it is not original, I cannot buy OEM because the price is very high. I have a replacement, I installed a new one before the renovation and it worked for 10 hours, like any replacement, the only adjustment is the fuel dose at idle speed. Before and after the renovation, I can turn the adjustment screw as much as I want without any effect, it was the same with the previous carburetor. Additionally, it is a slightly different carburetor than the recommended one.I should have carburetor 699831 (Nikki) or 799728 (Walbro) but I have a carburetor that replaces 593432, 794653, 791266. This carburetor is dedicated to Briggs & Stratton 12.5 hp overhead valve and my engine is a flathead. Could a slightly different carburetor be the cause of my problems? The old carburetor was also a replacement but dedicated to my model and the same problems occurred, I replaced it because it was worn out and fuel was leaking into the engine.
Please advise what may be the cause of poor engine operation and hot exhaust.
I am attaching photos of the new spark plug that worked for an hour after the renovation, and a short video showing the uneven operation of the engine, I tried removing the filter for a moment and blocking the air supply to check how the engine works when the air-fuel dose is richer, unfortunately I lack the knowledge and experience for this video and photos to helped me diagnose the problem.
So, to sum up, what could be the causes of poor engine operation and hot exhaust?
Damaged ignition system? I can't buy a new one without being sure because it's expensive.
Bad carburetor? I can buy a suitable replacement for my model, but still only with one screw adjusting the fuel dose at idle.
After the renovation, the engine was running for an hour while mowing large grass, then I noticed a problem with a hot muffler.
I cannot mow the grass because I am afraid that bad combustion and high temperature will damage the engine.
Could there be any damage to the engine when it worked for an hour with bad combustion?
The video was recorded when the engine warmed up a bit.

The fuel filter looks like it’s for a fuel pump. Looks like it’s running too lean. Was governor reset when the new carb was installed

You should be able to push the choke lever on at least partially on.
 
Do so and see if the missing clears up at all.
Running lean will definitly make the exhaust much hotter.
 
Also, do a Leak down test on the engine.  We need to know how much that exhaust valve is leaking.
If the valve is open enough, I would think hot combustion gases (that should NOT be exiting yet) 
could be making that muffler glow...
 
.
 
 

After market carbs, could be exact for the machine, however it's a 50/50 shot it'll work correctly.
 
The Chinese manufacturing is shoddy at best.  
 
Also, crank the engine, with the spark plug out and grounded. Make sure it has a strong spark 
when cranked over.  Obviously, make sure it's a known good spark plug. 
 
It sounds like you have most everything else covered correctly...
 
.
 
 

I installed a new ignition coil, it has 10.2k Ohm, the spark is much larger, the engine starts better and works much better, although not perfectly. I also poured more expensive fuel with 5% alcohol instead of 10%, because Briggs recommends increasing the fuel dose by 25% if the fuel contains 10% alcohol. This is a large increase in fuel dose for a carburetor that does not have fuel dose adjustment. Unfortunately I cannot buy alcohol-free fuel in my country. The engine runs better on 5% fuel, it's worth paying extra. I mowed large grass for 30 minutes, after that time the muffler would be orange, now even the inside of the muffler is not red. The engine still does not work perfectly, every few seconds one burst of the mixture is not optimal, the engine seems to stop a bit and a 1-inch flame appears from the muffler for a fraction of a second. I think I know what the reason could be, I checked the wedge locking the flywheel, it is slightly deformed, these thousandths of an inch on the wedge translate into a 1/8 inch delay on the magnet wheel relative to the engine. Does it mean that the ignition is too late? I will wait a few days for the package with a new original wedge. Maybe this will fix the engine stuttering problem. I also bought a tachometer to check the engine speed, the measurement surprised me, I checked it several times and the meter always showed the same result. The engine is about 3050 rpm at full throttle both without load and with load, it should be 3600rpm.
What could be the reason that the engine does not reach nominal speed? Is it because of the carburetor and too little fuel?