Hello and welcome to the forum
I would start with giving it a service if you haven't already. Unless you have records or completely trust the last owner you'll have little/no clue as to when it was last attended to.
So yes, I would start by checking the valve clearances, then adjusting the carbs sync.
Does sound to be running too rich, but this may be sorted by just doing the above.
Doing short runs around town on a regular basis isn't good for your engine. The constant stop start and the fact it won't get upto propper working temprature on a run will all have effects on the engine and fueling.
Bullet5.