I'm not sure about the fuel dripping from the needles, but your issue with the engine starting and stopping after a few seconds is exactly what my 3W-50i was doing a few weeks ago. I literallly spent two days flipping the prop till by arm and shoulder were sore and stiff! Fuel was dribbling out the carb, I had to pull the plug every few minutes to drain the excess fuel -- it was awful! I sent the motor to Cactus and they pulled the carb and isolator block and sealed the joint between the crankcase and the block with Loctite 518, which is an anaerobic gasket maker, and that engine now starts easily and runs beautifully. Yesterday I started it up on the stand, just to enjoy the ease of starting! I am going to give all my gas engines the sealant treatment after this. Bobby cautioned me not to overtighten the bolts holding the block on, so when I resealed my other 3w-50i block, I just snugged them to tight and used some loctite blue on them. If you haven't tried this, it doesn't take long and may make a difference.
Good luck,
sam