Thanks @CX, if I recall, I reviewed the latest Schluter spec and it includes greenboard - I will double-check.
@makethatkerdistick Thank you, yes, I am fairly assertive but I also want to be open to their experience. I am leaning toward pushing on something besides greenboard. Indeed, the tiling work will be of pretty high quality, mitering, good grout, and warrantied work. I appreciate your point.
@jadnashua I would call this shower "lower midrange" in fanciness. Floor-to-ceiling tile at 9ft, but no fancy plumbing/fixtures.
@PhilWA, that is a great way of putting it... if I knew I could commit the time, this would be the key argument for me to DIY it (three times, too!)
In the end, I've decided to grit my teeth and go with the contractor - mostly due to my own time commitments and what I suspect will be some unexpected surprises.
I will certainly be applying everyone's advice here, thank you very much.
I will report back when the work begins and progresses, just for infotainment. Assuming I can still pay my Internet bill.