I love the idea for your living shade structure, that sounds like an excellent strategy for your climate. You can probably use glass in your case as well (so long as you don't get hail). Often you can find old glasshouses that are no longer being used and offer to take them down for the person. This results in a really nice long lasting greenhouse if you have the time to put into it.
I am not a big fan of the dome, in my experience greenhouses are most benificial at higher and lower latitudes. For these locations the dome is not the ideal glazing structure as the sun is always coming from the south (when in the northern hemisphere). I prefer all of the glazing to face south, northern facing glazing is a big heat sink, as glazings by nature are not very insulative and in northern latitudes the sun never comes from the north.
That being said with an
Earth Powered Greenhouse (dug into the ground) you could grow tropicals without any energy, because you are fortunate to most likely get enough winter daylight hours. For your climate the earth temperature would be even more beneficial in the summer (providing cooling) than in the winter (when it provides heat). With all south facing glazing this also provides a strong thermosiphon at the ridge of the greenhouse. This is the pump that drives the passive ventilation system. The hot air rises, expands the venting arms and leaves the greenhouse. The resulting negative pressure draws outside air through the ground (via earthtubes) and then into the greenhouse, providing passive cooling and dehumidification. In my experience dome structures are tricky to vent, as only so many panels at the top can be vents.