Briggs sychro balance help

I have got a briggs synchro balance 10hp engine which I have was having a few problems with.

I was having an issue with the engine running properly because it has always had a slight misfire. I have tried everything with the carb and even took the restriction plate out of the box type exhaust but I have just found after taking the sump of that the cam gear was out by one tooth on the crank gear.

But the main thing is it has a had a slight knock on start up after being left for a week or so, which Im not sure whether its normal.
I checked over the engine and found the eccentric cam has slight play in it and is it supposed the be like that or is it supposed to have no play?

Another issue is just before I had it apart it was blowing out a little bit of smoke that looked like it was blue but only really noticeable in a small space in the dark with a torch. The cylinder appears to be ok and it had good compression so any ideas on that?

Just my 2 cents but I wonder if that cam gear put itself out....looking at that pic seems to be a lot of play there?...had a case of this before nearly drove me nuts....engine would run fine for a while only to throw timing out again...When I part reassembled block to ensure that both shafts were in line with casing the play was to much....on a cold engine it would fire up with a knock...poor crank seals and a constant half oil starved machine was the cause with this customer! ....check your cam shaft lobes too...

When these engines get old, excess play in the balance eccentric bushings is common and impractical to repair as both bushings and eccentric are likely worn plus the looks of that camshaft to crankshaft gears would lead me to replace the engine.

Walt Conner