FWIW, Shimano offers only a twist grip shifter for their Nexus 3-speed. SRAM offers only a twist grip shifter for their iMotion 3-speed. Sturmey offers a twist shifter, two kinds of thumb shifters, two kinds of trigger shifters, a bar-end shifter, a downtube shifter and a dual paddle shifter.

Neither Shimano nor SRAM offer any IGH internal parts support in N.A. You can get any part you want for a Sturmey.