Synthetic gear oil is pretty expensive. I can only find it in 75W90 where I live, and it is about $30-40 a litre. Conventional Castrol Hypoy C 80W90 is dirt cheap at ten bucks a litre, and a single litre bottle will last you many changes; the bottle says for motorcycle, ATV and scooter transmissions. I don't think there's much to gain from running synthetic, since conventional high pressure gear oil has lots of smelly but potent molybdenum disulfide added to prevent wear. Miami is also pretty warm, so I don't think you would need a thinner synthetic 75W90 too.
In Canada, it's Castrol Hypoy C. I also see it sold as Castrol Axle or Axle Limited Slip 80W90 in the US Catalog. They're rated API GL-5.
Joe, are you looking for engine oil or transmission/gear oil? The wet clutch concern comes from automotive engine oil in motorcycles with a wet clutch. Motorcycles often share engine oil with the transmission. I would definitely use synthetic engine oil in my Downtown though!