in simpler terms, you want more oil in your mix. you've been using 50 parts gas to 1 part oil, or 50:1. i'm suggesting you "raise" it to 2 parts oil, or 50:2, or 25:1.
i've tore up a few scooter 43's & 49's on my bikes, they're cheap & fun to abuse, but they have many weak points. if you start with a new one, and use a GOOD oil (i recommend Lucas) you can get a decent lifespan with a 32:1 mix. but that old beater needs lotsa oil if it's gonna keep running for you, especially after scraping along for 1/2 hour with hardly any. just my opinion is all, hope it works out for you.
yaknow, i had meant to ask, is the smoke coming off the engine (which is how i interpreted it, as being overheated) or from the exhaust? i ask because, altho you do need to increase the oil, you may also have a carburetor adjustment to make.