Anyhow the frame rear spacing on the cross check is 132.5 mm to accommodate either road or MTB hubs, but with a few washers to space the axle out the S3X fitted up rather well and with the bar mounted thumb shifter the operation is very smooth.
I routed gear the cable down to the right hand braze on , under the BB and straight to the chain stay braze on where I used my preferred method of holding the gear cable in place. Cut a section of gear cable outer , I always use Jag wire at the shop as its good quality and comes in a wide range of colors . The section of cable outer needs to be about the same length of the black plastic or metal cable end cap and should slide into the braze on very easily. This alone would not work and with riding would only work its way loose causing the cable to wear against the braze on. But with a little Kiwi ingenuity I purchased a can of Mellow Yellow ( Yes you can still buy this soft drink here in Japan over the summer ) and because it is a soft alloy can you can easily cut it with a pair of scissors and use a very small section of the alloy as a spacer to hold the cable end cap tightly in place. I have used this method now on 3 occasions for Sturmey archer builds without any trouble as if you are very careful you cannot see the alloy tin spacer and the end cap with the section of outer will stay tightly in place and allow the cable to slide easy when the gear is operated. Pictured below is the cable end cap and the Sturmey archer toggle chain fitting
So if you are wanting a colored hub on your 3 speed ,you can indeed use the S3X fixed hub with a standard free wheel. The hub comes in several colors and matching front hubs are also available as well.