This Sturmey Archer hub is an internal gear hub and as all internal gear hub, it will require some torque blocking system, i.e. something that avoid that the hub axle turns wrt. the frame dropouts (its the special parts that R&M add to the Rohloff).

Did you test the Birdy with its 9-32 cassette as it is now ? Is it really too limited ? Or did you already replace the 9-32t 356% cassette with a smaller range 11-36t 327% cassette ?

I would never add such an heavy low efficiency hub to a Birdy !