It is very intermittent.
It sat all last night without leaking.
It then leaked at some point this morning.
I have not touched it.

Also...everything was very clean inside when I took it apart.

I am stumped!

I have had the same experience, twice. The cause of the first problem was a damaged seat. Gas was slowly getting past it and flooding the carb. The seat was only 2 years old and it was cracked on the grooved side. The second time on another piece of equipment with a 6.5 HP Briggs, I suspect dirt particles from either the gas tank or crumbling inside the fuel line . This caused an intermittent clogging and flooding much more severe than the damaged seat. The only other thing I can suggest is make sure the seat is pushed all the way down ( groove side down ) I seem to recall instructions saying to use a drill bit flat end to push the seat down.

Is it possible to install a manual fuel shut off valve between the gas tank and the carburetor. It sounds like the leak is only causing a problem during storage. A shut off valve, opened for use and closed for storage would resolve the problem, if there was room to install one.

I also had a similar problem and the replacement seat was bad too! 2nd one worked.

Remember if you get a new seat or remove there is a up and down on the seat installation. The ring on the end goes to the carburetor base not the needle.