I replied last night, but it hasn't shown up yet, so I'm sending it again. Hopefully it won't post twice.
How does your air filter look? Has that been changed recently?
You definitely should gap the plug correctly, but cleaning it after every use is a little excessive.
There are several types of buildup that could be on your plug... It could be from bad gas (unlikely since you just put in fresh, right?), or running rich (which you seem to know how to adjust), or also you could be burning oil. That could cause the buildup on the plug in that short amount of time. Has the oil level gone down as you use the splitter? What kind of oil are you using in the engine?
Are you operating the splitter at full throttle, and is the choke all the way open when its running?
Air filter looks like new. Actually, it might be. My dad replaced a few things when cleaning it up for me. I know he put in a new spark plug at the time. The only issue was he over oiled the filter, so for the first couple hours of running, it was struggling a bit for air. I've since squeezed it out better into paper towels, so that should be fine now.
The spark plug will end up with a liquidy black residue around the edges near the threads. More solid (or dried) black matter where it fires.
I've used a couple types of gas. The problems started when I was using 89 octane that was fairly fresh (couple weeks old?). My standard is to get 2.5 gallons of 89, add Stabil and Marvel Mystery Oil to it. That goes into all my power equipment around here. So it's usually pretty fresh, especially in the summer when my lawn tractor is guzzling it down. I had run the splitter for at least 4 hours this year and a few hours last year with that type of gas. I was well into my issues, when I ran out of that, and switched to some older (few months) gas, 87 octane with Stabil, that I had around for my plow truck. I've been using that since, knowing that I should use it up. I could just dump it into my SUV and get some new 89 octane. I'll try that tomorrow. Nothing else is complaining about the gas I've been using, and both types had the same result.
I'm not sure of the exact oil type. My dad changed the oil before giving me the splitter late last year. I took off the cap on one side and the level is right up there and when I dipped my finger in, it came out looking pretty clean, for oil.
I'm not sure where the throttle control is, for setting the speed. I pull the choke out, pull the cord a couple times and it fires up and sucks the choke back in. That's where it runs. Under load, the throttle increases, when you ease off, it drops back to idle.
I'm hoping to run it Saturday and see how it goes, with a clean cylinder, and much cleaner valves. I'm curious if I'll see the same behavior with no issues for the first 90 minutes, then if it starts to stall under load. Also, it's not just about running it cold. I had issues before and shut it down for a couple hours. Within minutes of firing it back up the troubled behavior was back.