Originally Posted by don d.

The Shimano 105 headset has 32.7mm to 33.3mm stack height, depending on the model. The headset with the smallest stack height is the Tange Passage headset, which has a stack height of 30.2mm, including keyed lock washer. You get ~1 full turn of the locknut for every 1.5mm of stack height you eliminate. The Tange headset is available online for ~$15.00 from Harris Cyclery or Branford Bike.

You can eliminate the keyed washer on your current headset, but you should use two headset spanners to tighten the upper cone securely against the locknut.

Milling the frame will cost you from $20.00 to $30.00, depending on the shop doing the work. It will also permanently alter the frame, which may mean something or nothing, depending on how it's done.

The steerer can be cut and an insert sleeve brazed into the steerer to extend the steerer, but that would be rather an extreme and expensive solution. It sounds like you're close enough for the Tange Passage HS to solve your problem.