I would take your bike to a bike shop and see if a Sturmey Archer Hub can even fit on those axels. It may not be wide enough!
Also, the AW-3 is not really ment for aggressive off road because the transmission can slip. You're not supposed to stand on the Sturmey Archer 3 speed for similar reasons. If you are buying new, why not buy the one with the coaster brake?
Oh, by the way, nice bike.