Well I can say one thing. You are persistent. Most people would have given up long ago and hauled it to the landfill. It sounds like your scooter was not very well treated or maintained before you got it. I have a Yamaha Vino 125 that I bought new, which now has over 20,000 miles on it. It is still like new. I have never had a single problem with it, other than the fuel line and vacuum petcock. I have replaced the fuel line about 4 times, and have completely done away with the petcock. It was an inline design, in the fuel line between the tank and carb. I just ran a straight line from the tank to the carb. I can pinch it to shut off the fuel if I need to. Surprisingly the needle valve has not started leaking yet. Maybe it does not have a rubber tip on it like most of them.
Real gas is impossible to get around here. There is a marina about 20 miles away, but they only sell the 10% moonshine gas too. Local airport will not sell avgas unless you are putting it into an aircraft. The only source of real gas is the local dragstrip, and the stuff costs $9 a gallon, not an option. Ethanol gas is bad stuff. I am pretty sure it destroyed the plastic gas tanks on 2 honda dirt bikes. They developed cracks all over. It also turns rubber to mush. It will damage any rubber fuel line, vent line, and any rubber parts in the carb. It also tends to destroy the packing in manual petcocks and the diaphragm in vacuum petcocks. It melted the diaphragm in the fuel pump on my '72 Pinto.
If your scooter has any kind of emissions crap on it, I definitely recommend getting rid of that. The fuel tank should be vented directly to the atmosphere, no into a cannister. Make sure you carb float bowl vent is open. Make sure your crankcase vent is not restricted. Many bikes have a "separater" in the crankcase vent system, designed to separate liquid from vapor. There is usually a long tube with a plug on the end of it to catch the liquid, which is usually a combination of oil, gas, and water. It is commonly called a "puke tube" and needs to be drained every so often. Or you can just leave the plug off.
Unfortunately, motorcycles and scooters do not yet have positive crankcase ventilation systems like cars, they are usually vented to the airbox. Cars from 1962 on use actual engine vacuum to suck the vapors out of the crankcase. Don't know why this won't work with bikes. The Honda Met and Ruckus from 2002 through 2005 had a very poorly designed venting system, most of these engines did not make it past 10,000 miles. It was redesigned in 2006.
If the carb gets all gunked up again (it has to be engine oil, nothing else it could be. thats why I don't understand why spray carb cleaner would not dissolve it) try connecting a hose directly to the crankcase vent fitting, and leave the other end open. As was said, a single or 360 degree twin (which is basically a 2 cylinder single, both pistons rise and fall together) inhale and exhale through the crankcase vent. In a 180 degree twin, where one piston goes up while the other one goes down, they cancel each other out. They also don't vibrate as much. A more efficient design all around from an engineering perspective, but somewhat lacking in character.