Your circuit is a half decent regulator and would be good for powering most things that need a small current. The problem, as you quite rightly point out, is the 0.7V lost between input and output.
Low drop-out regulators are really quite common-place and some work really well down to a few milli volts between input and output BUT, they are far more complex than what you think and cannot be made from a couple of transistors, a handful of resistors and a zener diode.
However, in pursuant with your wishes, the best idea I can come up with is to construct a small single transistor colpitts oscillator that runs from the incoming power supply and, via two capacitors and two diodes can create a voltage that is bigger than the incoming voltage - this can then feed the zener diode via a resistor ensuring that the BJT is always biased on at the zener voltage even when the supply is quite close to the zener voltage.
Probably the best you could hope for is a volt-drop across the transistor of 0.1 to 0.2V - but that is better than 0.7V but not as good as some commercially available devices from the usual vendors.