Equivalent Centurion BB?
 

I have a 1985 Centurion Sport DLX. Sugino No. 6 Crank (double, 52T outer chainring)

I'm trying to find a modern replacement bottom bracket that will fit the frame (and crank, if possible) that has the same pedal position or slightly wider on the crank side.

I am unable to get an exact measurement, since I don't have the right tools to remove the cups properly...

A couple bike shops in my area, which will remain nameless, looked at my existing BB and had no idea what to make of it since it has the old asymmetrical cup and cone style. Some posters here have suggested a 68 x 127 will fit for a triple crank. Would a 68 x 122.5 or 68 x 123 fit for a double?

Has anyone else done this upgrade to a similar bike?

I responded to your question in the mechanics' forum, I'm the one who referred to the Sugino triple crank (Sugino AT) using a 68 x 127 bb. But I was just giving an example of that particular crank, and how I had used the old bb spindle, which gave a good chainline, to determine which cartridge bb to get. The bottom line is that, assuming the existing spindle is the correct length, you should use that to determine which spindle length to use-:)