Check the woodruff key as Jim suggested.
Is there a wire or something sticking out and causing an obstruction or something in the groove around the perimeter of where the fly wheel should seat?
Give it your best shot of aligning the slot in flywheel cover with the woodruff key in the shaft. Then rotate the shaft so it turns the flywheel. Stop and jiggle it a bit to see if you can get it to seat. Repeat this a couple of times. Sometimes I have to pull the cover again and try it a couple of times to get it to align and seat. If you think you have it in place, then while it is still lying flat, screw the black plastic cover on to hold the flywheel in place.
Don't know what else to suggest unless you want to ship it to me and I'll check it out at no charge. You pay the shipping both ways (about $20-$30) UPS ground. Or you could take the engine and flywheel to a motorcycle shop or a small engine repair shop(lawn mowers) to see if they can figure out why it won't seat.