I have my own reservations about shimming. Why do you think shimming is a bad idea?
The bottom bracket is a Phil Wood. It has already been set to the left about as far as I am comfortable doing - the left retaining ring is flush with BB shell, the right retaining ring protrudes two full turns of the threads, approx. 0.05".
IIRC, the spindle is 120 mm long with a two degree taper. The bottom bracket shell is 68 mm wide.
I am not averse to buying a new Phil BB with a longer spindle but they do cost $200. What I worry about with that option is spending the cash but not solving the problem. After all, we are talking about only 0.004" difference.
I think the next step i to ensure the chain rings and freewheel are properly aligned.
Could it be a crank problem? Is the square-sided socket mis-shapen, stretched or something? It is a vintage Campagnolo NR crank but is new to me (my first use of this crank). Could it be a different taper than my spindle?
What should I do after that?