I run multiple modified strada cranksets, and have encountered the same problem.
My 70-P-120 (109mm) which i had used with great results on a 151 BCD dura ace track crank (it has the same bearing race distance as the 68-S-107 (NJS) dura ace spindle) would not work.
On a 68mm BB shell I use a spindle with a medium bearing race distance (e.g . for 70mm shell and thick walled cups) with a thin walled cup on the right, and a fat one on the left.
Obviously this will not work with the 70mm BB shell.
For lack of other options (or cups) I use a 115 or 116mm Shimano Spindle on my french threaded bike. I need the length for the crank arm to clear the right chainstay, but it results in the left crankarm sticking out a bit.
Ideally I'd use a BB with a short spindle (around 110mm) with a BB that let s you adjust the chainline.
Good luck,
Tobit Linke, Dortmund, Germany