Wait a minute - you're talking about not "some undefined IGH" or even "some SA hub", but the new, yet to be released, nobody's ridden one, internal design and cable pull unknown, first in 40 years, multi-speed fixed gear Sturmey S3X? And you want advice on how to use a shifter other than the two proprietary offerings with this unique hub?
Yeah, I think you're going to have to tell us what works if and when you get it all worked out.
Best,
tcs