Hi Jai,
From your description, the first thing that comes to mind is valve stem seals. They are little rubber seals around the valve stems that limit the amount of oil passing through to the valve guide to a minimum. If the become old, they harden and break and allow oil to run down the stem and throught the valve guide to the inlet valve. The inlet valve is mostly under vacuum and causes the blue smoke problem after a period of coasting and the acceleration.
A simple test would be to coast down a hill with no throttle and at the bottom of the hill a short burst of full throttle or hard acceleration. You should see a plume of grey blue smoke. That is a good indication.
Why the test: When coasting, high vacuum pulls in more oil then normal, but a closed throttle doen't give it enough fuel air to burn the oil. When you give it full throttle, the fuel air mixture then burns the oil creating excessive smoke for some seconds.
A compression test will tell you more about the overall condition of the engine.
A bit hard to say if the putt putt sound was there before or not, since the muffler was changed, makes that hard to say with any certainty. And you mention the exhaust sound is more noticable with the new muffler.
The smoke issue could be all some time, but it has now come to your attention due to the sounds from the new muffler.
Goodluck with finding a solution Jai.
Regadds
Chas