The only way fuel can get into the bowl is through the float valve, so it has to be the float valve or the seat that it closes against. Did you pull the seat and replace it? I know guys will blow compressed air through all the passages of a carb when cleaning them and blow out parts they didn't realize.
What i would do, pull the carb, drain it, put a piece of fuel hose on the carb and blow into the hose while playing with the float and valve, move it up to what would be the closed position, are you still able to blow air through? If so then its leaking, pure and simple quick and easy test. Replace the float valve and seat, or just the seat if you already replaced the valve. Then test again. If you can hold the float up by hand and it seals then try again with fuel, you don't even have to mount it up, just sit the fuel tank on the edge of the workbench and hook up a length of fuel line to the carb and hold it over a bucket, thats how i test them before tossing back on the motor. If its still leaking then it must be the float is not pushing it up far enough, a new aftermarket float with an adjustable tab for the valve would fix it.
Leaking carbs suck, but they can also cause major engine damage from diluted oil and running too rich. There is a new replacement carb available to replace it on eBay for like $30, you can buy a new one for not much more then a rebuild kit these days. I still like to rebuild if the slide is not worn out, but sometimes a new carb is just the best option as they do wear out.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....