I'm getting a proper road-triple chainline (~45mm as measured to the middle ring) using a Sugino XD600 with a 110mm bottom bracket. Keep in mind that the 110mm BB is asymmetrical, and has the same drive-side extension as a 107mm BB. (the extra 3mm on the non-drive-side is necessary to get the non-drive-side pedal equidistant from the frame's centerline).
Here's a thread that I started a few years ago about symmetry of standardized (sealed-cartridge) square-taper bottom brackets.
From my measurements I think you'd be fine with a 113mm bottom bracket.
According to Sheldon Brown's bottom-bracket size database, the Sugino AT takes a pretty wide bottom bracket spindle already. which would be a reason for going with the XD600.
Shimano UN-54 - $20.
When that fails (and the Shimano sealed units have reputation for holding up really well) you can get a $100 unit.
I seem to actually remember that 107mm is slightly asymmetrical in the reverse, with drive-side spindle being 1mm longer than NDS, while 110mm has NDS 2mm longer than drive-side.
When I compared a 113mm to a 110mm this morning, at my desk (pulled some extras out of a box) the 113 actually seemed comparable spacing to the 110mm, but slightly wider on both sides. Should have clarified this better in previous post.
I have no idea if the SKF bottom bracket follows the same spacing as Shimano units, but most JIS BB's made nowadays probably do. For it to be worth that price, maybe it should have adjustable chainline (like the Phil Wood units).