the "4' tall roof over a 6' underground structure" is not actually that extreme. there are a number of people creating passive greenhouses that match those parameters. They also tilt the south facing windows to be perpendicular to the sun at it's lowest angle (winter solstice) for maximum light penetrance aan solar gain in the winter and maximum solar deflection in the summer. They are called Walipinis and some of them really are a hole in the ground with a small roof overhead. here is one built for $300:
Build a $300 underground greenhouse for year-round gardening (Video) : TreeHugger