I had/have the same issue with my old Tote/Cycle. From my investigations, the Sturmey-Archer 8 was the only way to go. I believe there was also a SA 5-speed that would fit, but the price between the 5 and 8 was small enough that I didn't really consider the 5 an option.
But, in my case, I ended up staying the 3 speeds because I needed the coaster brake and while I think there was a SA 8 with a coaster brake, the addition of the brake made it too wide.
So-- no integrated brake: I think SA8 is an option. Integrated brake: maybe an SA5, but I don't know for certain. The price jump between 3 and 5 was such that I didn't really think it worth investigating.