You did not mention having replaced the spark plug, or even cleaned it. It was probably quite heavily oiled back when it was smoking, and it will not clean itself unless it has a longish run at heavy load.
If you are not used to Briggs and perhaps other side-valve engines, you need to bear in mind that they do not scavenge well. I can rather reliably distinguish between side valve Briggs engines, and OHV Honda engines, from one to two hundred metres distance without seeing them, just by listening for missed shots. OHV Hondas do not miss shots, side valve Briggs engines always do, especially at idle, but it is noticeable any time they run at light load.
A very slight irregularity such as you have described could also be due to poor valve sealing. You should check the tappet clearances, and while you are at it you could clean the crankcase ventilation valve, since it is built into the valve chest cover that you have to remove to get at the tappets.
Removing the muffler and inspecting it for clogging is a relatively low priority check, especially when you have not yet made the other checks listed, or run the engine under sustained heavy load. However if all else fails, you might remove the muffler (use an oil filter strap wrench), check it for carbon fouling, and run the engine without it, so you can watch for a flame from the exhaust when it falters.
My best guess at the moment is dirty spark plug, or just the normal side valve irregular misfires.
