hi peter,
to find out the valve clearances we need to model type and code numbers found on the cowling of the engine. also is the engine a over head valve unit or a l-head block. from the description it sounds like it is a OHV but we need to be sure.
as to the carby and running problems there are many possible causes, but if re-adjusting the tappets does not fix it i would consider putting a carby kit through, especially if it is leaking fuel.
i agree with you though that the resistance during starting is caused by sloppy valve clearances as briggs and stratton design the cams so the exhaust valve is slightly open during to compression stroke so it is easier to spin over. they say there is no effect during running though, which i am a makes me qringue a bit.
anyway good luck!
regards jay