I've ordered the Hablitzia (Caucasus mountain spinach) breeding grex seed pack from the Experimental Farm Network, but have yet to receive my seeds, so I can only comment on what I've read, not yet having direct experience.
The first thing that comes to mind is that Caucasus mountain spinach is generally described as a shade-loving understory plant, so it may not be happy being in full direct sun all day, depending upon your climate, and how hot your summers are.
I'm in the foothills of the Appalachians, on the western edge of the Highland Ridge of the Cumberland Plateau, so our summers are very hot and humid, often topping 100 degrees Fahrenheit.
I'll only be planting it in shady spots, at least in the beginning, under large trees or along pathways in our woods behind the house.
Keep in mind also that in its first year, Hablitzia grows only a rosette of leaves, close to the ground, and doesn't start vining until its second season.
I love the idea of a vine covered shade teepee, but at least initially, I'll be planting mine with Scarlet Runner beans, as they may possibly be perennial in my Zone 7b garden, although that too remains to be seen.
Good luck with it, and keep us posted, as I am hoping for a longstanding relationship and ultimate success with Hablitzia.