As everyone has noted, ring failure is the likely culprit for the blue smoke but there several reasons the rings may have failed.
You have not told us how long it has been since the last rebuild. If it is fairly recent, it is possible that one or more rings have been put in upside down (modern rings often have a camphered top outer edge, if upside down, oil will pass into the combustion chamber). Too tight a ring gap can cause a ring to break and score a cylinder. Too loose a ring gap and oil will pass through the gap. Improper ring gap alignment between upper and lower ring will also allow oil to pass into the combustion chamber. Incorrect ring size (example, using a .050 ring on a .040 piston) will not be round (it will be elliptical) and will not seal the cylinder properly, quickly wearing out.
Fuel mixture, too rich will cause premature ring failure by washing the lubrication off the cylinders. It will also allow carbonization of the heads causing poor performance.
Too lean will cause overheating and can eventually burn a hole through the piston.
Only a proper medium mixture will give best all around performance, neither lean nor rich.
Spark plugs, is it possible you have been running a plug too hot for your driving conditions?
Is your carburetor an M-88 with a fixed high speed? If yes, is the needle fully seated and is it running the correct #1 jet? If not, this could be a source of running too rich.
On the M-88 with the fixed needle, the adjustable low speed needle effects only idle operations and light load operations under 35 mph. No impact on the mixture over 35 mph.
Sluggish operation (poor carburetion and bad rings aside): proper timing is a must. Are you doing your timing with or without a test light? If you are not using a test light to establish exactly when the points break, your timing may be off (I say “may be off” because you might accidently properly set the points).
Point gap is a snug .022”. Plug gap is .028”.
Electronic ignition? Personally speaking, a waste of money. They can and will break down. Heat is their enemy and heat is what they get riding inside an H-D breaker housing. Points can be cleaned on the fly to get you home.
If you running the H-D early style points, make sure that the points are tungsten. Some aftermarket makes are cheaping out on the material. Also, with the aftermarkets, the moveable point may have flashing at the pivot point which needs to be trimmed so the point sits properly on the post. Also check that the fiber block is square and square the points as well to get a proper gap. You can also run the 1949-1969 style points (a readily available GM point set) by converting the breaker head to the later points (a friend has a pattern and does this upon request) or by converting to the later 1949-1969 breaker head.
Additionally on your performance and points, look at the points themselves, are they burning cleanly or is there transference of material from one point to the other? Depending on which point is getting the material will indicate if your condenser is too strong or too weak. Regardless, if transference is occurring you will need a new condenser.
Back to the ring failure, it can also be caused by a dirty air cleaner. Further, now that you have blue smoke, you are also likely experiencing “blow-by”. Blow-by is the combustion gasses passing the rings and getting into the lower end. The heat of the blow-by gasses are too intense for the lower end bearings and will lead to a premature failure of your rods and flywheel shaft bearings.
One more possible source of ring failure is a bent rod. When you pull your cylinders, examine the carbon tracks on the sides of your pistons. These tracks will be on the sides with your wrist pin holes since the pistons are cam ground with the wider surfaces front and rear.
A straight rod will have a fairly straight up and down carbon track with slight flaring at the top and bottom. A bent/ twisted rod will have a track running at an angle away from up and down. If you have a bent/twisted rod, you will need to take of that before changing out the rings/pistons or you will be in exactly the same boat you are in sooner then you want to be.