I would move my engine plate over the whole 1/2" it needs to go. cut the welds or cut the plate, your choice. Use some flat stock as filler if need be. Imo it's the quick dirty, cheap, easy way. Looks like you just mismeasured.
That's not the problem.... This isn't a home built kart. Its a factory bent and welded chassis. With that being said, its a culmination of many things,causing the misalignment.
First off, you need to go to the hardware store and buy 2 washers with a 3/4" id and that are 1/8" thick. They cost like $0.85 each at home depot. That's what I use. You need to space the clutch out to the end of the shaft. That's 2 washers, or a 1/4".....
Next, there is probably a washer between the hub and bearing, or a couple. If you can, remove them . If that's not possible, use a nut as a spacer, between the sprocket and where it bolts up. Doing this and the first thing, gives you a bit more than a half inch...
You should also use nuts to space out the brake drum, in typical Manco fashion....