30-35 at half throttle is pretty fast for a stock puch? that doesnt seem right
i am running a 64 with the standard airbox, does your plug look like coffee with cream in it? If it dies at full thottle that sounds like its getting to much or not enought of any part of the fuel mixture, probably to much air
i would suggest going through all the standard moped procedures, clean exhuast port and pipe, set and clean all points, throughly clean carb, ect.
then get a variety of bing jets and start small and run through the numbers untill it starts to feel right, if you get to a jet that allows the bike to run and feels all right, then ride it around and do some plug chops, make sure you have the correct ratio, once you have a general idea of the plug area you may have to move up or down to fine tune it,
and remember, a really big jet doesnt always mean the bike will work fine,