Your lower crank seal is very likely it, and the running symptoms line up. On a two stroke the crankcase is the primary compression chamber, so a leaking lower seal pushes oil out and pulls air in on the upstroke. That extra air leans the mixture, and lean is what makes one sputter and die the moment you put a load on it. That's also why cleaning the carbs twice, replacing every fuel hose and the filter, and checking the diaphragm didn't change a thing. The air is getting in downstream of all of that. One thing before you run it again: don't. A lean condition under load is how these melt a piston, and a melted piston turns a seal job into a rebuild. On the two seal types, yes. There's a press-in style you can drive from outside once the lower cover is off, and an inner style that sits behind the bearing and needs the cases split. Get the powerhead off and see which one you're dealing with before you order parts. While it's apart, plan on the base gasket, the reed valve gaskets, the intake gaskets and the exhaust cover gasket. And feel the crank journal where the seal rides. If it's grooved, a new seal won't hold and you'll be doing this again next season. FWIW the clean blue/green is fresh injection oil, the black gunk is old oil that's been cooking on the case. Both at once says it's been weeping a while and just recently got bad.
