Maybe the seat is just buggered up and the needle can't seal?
I had a Homelite 240 that I almost just dropped a match in the gas tank and walked away from because it would do this. Turns out there was just some funk floating around that would randomly end up in the needle seat. It would be fine for days, then one day flood, leak gas out the muffler, etc. If I had an nickel for every time I had it apart, I could retire. Same fiasco with a 10-10 carb that had a loose welch plug. Everything looked good when I took it apart, and then finally one day the plug literally fell out. Must've been the factory sealant around the edges holding it in, but it never felt loose on inspection. That 240 starts and runs flawlessly now and I've actually come to like it quite a bit.
Anyway, might try checking down the needle hole with a loupe, or magnifying glass, or take a picture with your phone (+flash) and see what it looks like? You can zoom in pretty well with a digital pic if you can get a good light down there and get it to focus. FWIW, I got a cheap set of plastic loupes of different magnifications on Amazon and REALLY like them for this kind of stuff.
Have you been able to test pressure on it? I just use a piece of (new) fuel line and see if it'll stick to my tongue if I put a vacuum on it, or hold pressure if I try to blow air through it. You can usually hear it hiss if it's leaking, or put a few drops of wd-40 down there and see if it'll bubble. Gotta get a mityvac one of these days...
-Rich