IMO, it's not the points. You HAVE to be doing something wrong. You need to figure out how everything WORKS.
Don't just follow instructions, figure out what causes the points to open... so you'll know what you're actually trying to accomplish.
Look at the backside of your flywheel. In the center. There is a pipe lookin piece that sticks out. It is NOT round. It IS a cam...the "points cam". It has ONE spot that is high...a lobe...just like the actual head/valve cam has 2 lobes that cause the valves to open, the points cam has one lobe. The plastic lookin block on your points..."rubbing block"...RUBS against that points cam/lobe as your flywheel spins. Every time the lobe comes around and hits the "rubbing block" your points open.
When you set the flywheel...which is properly indexed on the KEYWAY KEY...to the "T". Not the F, the T mark on the flywheel, lined up with the mark on the engine case, exactly, and held there at top dead center, the points should be set to .016 inches.
After they are set, and before you move that flywheel, tighten the screw to keep your .016" setting. Then before you move that flywheel, double check your .016" measurement. Make sure it did not change or move when you retightened the screw.
Then, Spin the flywheel a couple few times counterclockwise. Then, set it on the T again. Hold it there. Then check your .016" measurement AGAIN. Make sure it didn't change. Then, before you move that flywheel, LOOK in there at your .016" gap...see that your points are OPEN... .016 inches. Keep looking in there, and move your flywheel slowly, counterclockwise, always counterclockwise, and WATCH your points CLOSE. Keep spinning the flywheel, a FULL revolution. When the flywheel comes back around to the T mark, your points rubbing block will be directly on top of the lobe of your "points cam"...on the inside of your flywheel, causing your points to be open again to your properly set .016" gap.