Since you already have the adapter taken care of, all you need is the BB and cranks. Most cranks will tell you what chainline they will give you for a given BB length. If you need to change it, mess with the BB size by twice as much as the move you want to make, and make sure you are getting a symmetrical BB. Since most bottom brackets are sized in 3mm intervals, you may have to use 1mm or 2mm bottom bracket spacers to get things right on. However, remember that a spacer moves the chainline by its entire width, since it moved the whole BB over.
Say you decide to use bulletproof cranks, which are a good, cheap option. As per Sheldon's measurements, the "inner" position would be 39.7mm with a 107mm BB, and the outer would be at 47.1. You're probably going to need to use the inner position for clearance reasons. So ideally you need to move the chainline 2.3 mm out . You could get pretty close by going up to a 109, which moves it out 1mm, and then putting on a 1mm spacer. .3mm ain't nothin' to worry about.
Disclaimer: old 1 piece crank bb shells are the standard 68mm wide, and I'm just assuming here that the converter rig maintains the shell width. It looks like it does, but I've never actually seen one in the wild.