Your post got me thinking about a way to buck a voltage down to power an LED
and eliminate the current-limiting resistor. This can be done when boosting--that's what the Joule Thief circuit does. I've never seen it done bucking, though.
I don't know if it will work but the attached circuit
might do what you want. In theory, it should buck or boost the voltage to the LED's V
F.
The closest I've seen to something similar is the
TRANSISTOR and LED TESTER - 3 circuit
here. You'll notice that the right-hand side of that circuit is similar to mine, with the exception that mine has the LED's anode tied to ground.
One potential problem with the circuit is that the LED's V
R would have to withstand 12V. A diode in series with the LED might be necessary. You'd also have to wind your own transformers if you use this circuit.
I'll test this circuit and let you know what I find out. Like a lot of my ideas it may be "too clever by half", if you know what I mean.