I’ve had those banana seeds in the greenhouse since January, so apparently it took about five months. Putting a lid on top seems to have been a necessity: the seller suggested putting the seeds ON TOP OF the soil, with a lid on top to keep the soil consistently moist and the humidity high. That seems to have been the way to go.
I’m not sure exactly how to replicate that with direct sowing, but maybe a living mulch? I’m wondering it if may work well to sow a whole bunch of peas with banana seeds in the middle of them. That way, as long as I water the peas, that may keep the humidity high and the soil evenly moist for the banana seeds. (And, let’s be real, I’m significantly more likely to keep the soil watered if there are plants that I care about there already.)
Good point that the greenhouse is going to get as scorching hot in the summer as the rest of my garden. And a lot of tropicals aren’t wild about 100 degrees of dry heat. Maybe keeping the plastic cover on year-round would be a good idea, since it would keep some humidity in there in summer, and that may be valuable.
I tend to think of shade cloth as “that thing you use when you haven’t figured out the right plants to use instead.” 
So I’d rather avoid it. Hmmmm, actually, now that I think about it, passionfruit vines climbing the metal framework would make for a nice, partially shaded space in summer and provide an extra layer of insulation in winter . . .
Moringa stenopetala on the west side of my greenhouse, in order to provide it some afternoon shade, too?