I had a chance to take the carby off today and took it apart as best I could to clean it. The only snag I struck was the main fuel nozzle, it was stuck in pretty good. I ground down and reshaped a flat blade screwdriver to fit the slot in the nozzle but still couldn't get it out.
Anyway, I cleaned it all out, poked some fine wire into the nozzles and gave it all a good spray with carby cleaner. The float wasn't quite set parallel so I reset that and then put it all back to together and re-installed it onto the mower.
Still no luck. The main issue seems to be that no matter how I adjust both the main metering needle or the idle mixture screw the engine runs way too rich. Today, after starting the engine, I wound the main needle all the way in and the idle needle into about 1/2 a turn out from fully seated and while looking into the throat of the carby I can still see tiny splashes of fuel landing on the sides. It's also obvious from the fumes and smell that it's running very rich.
The thought has occurred to me that maybe the float needle is not shutting properly and constantly allowing fuel into the bowl but I've replaced the needle and checked that the float doesn't have any fluid inside it due to a possible hole in the float itself. As I said above I've also set the float level as per a tutorial I've found on an American site for the carby.
I'm not sure what else to do. The only component I wasn't able to remove and clean was the main nozzle but I don't know that it could be causing all this anyway.
I've spotted replacement carbs on Ebay for $60 delivered. They're Chinese knock offs but I'm considering getting one and trying it. They're certainly a lot cheaper than the $250 or so I saw for a genuine Briggs & Stratton item.
Does anyone have an opinion on whether I've exhausted the possibilities with my existing carby and should be looking to replace it?