As a fan of square tapered cranks, and someone who could help advise you regarding spindles for that application, I have a suggestion.
Use an external bearing bottom bracket and large diameter spindle crankset akin to the way All City suggests the frame can be assembled as a "complete."
Unless you "need" to make this bike work with a 6/7-speed rear cassette, which seems doubtful given the 142-disc rear, I can't imagine how the Ultegra 600 crankset contirbutes to creating a cohesive drivetrain for this bike.
__________________
.
|