I havent dis-assembled mine to this extent, but Im pretty sure the problem is this:
The steam knob operates a needle valve made of brass. When it is hot (as in you are steaming) the brass expands a tad and when you shut it off, it stops. But then as it cools - the brass doth shrink and you get a reasonable squirt or dribble. To check that, you just need to nip the knob off a bit more when it happens. Stoppage implies this is the problem.
The other way of checking this is to steam and then turn her off and let her cool right down. Then turn her back on to warm up. A puddle under the steam wand is likely >:( Darn valve. Im 99% sure mine has gotten worse since I first had it, but I cant be sure.