I have nothing to add for the question asked in the title, but I do have a possible solution to your second/third points of how to overcome the 1.25V barrier. As you've probably realised, the voltage output of the LM317 is 1.25V greater than
Vadj, thus you need a negative supply to pull
Vout down to zero volts. I built a 5A dual supply a long time ago and got very good results until somebody dropped it when moving house. I have never got round to rebuilding it, but it was based around the circuit below. I have omitted the transformer/rectifying/smoothing components as they are nothing special in this case. The smoothed, unregulated DC supplies go to
It uses a few more of your hard earned money coins by using op-amps to provide a stable
Vadj, which in turn requires some sort of regulator to provide the +/- 12V supply for the TL074. Any regulator will do in this case, fixed or adjustable, over a fair range.
How it does the thing that it does:
U1:A buffers the voltage split through the variable resistor
U1:C inverts this so that
U1:B end up with equal but opposite voltages at their non-inverting inputs.
B are essential for providing a stable, high-impedance for
R2+/- (circled in red).
[If you want to have separate +ve and -ve voltages connect
U1:B+ to its own voltage divider, and leave
U1:Aout going only to
R2 resistors pair with their respective
R1 resistors and adhere to the standard
Vout equation plastered about the datasheets for this regulator and its cousins, except you then subtract the voltage
V_BIAS+ (or add the voltage at
V_BIAS-) to get the actual
Vout. It's up to you to choose values of
R2- - and also
R_ADJ - to give you acceptable voltage swings. Note that the
R2 values will not be the match due to the current
Iadj, which differs slightly from one IC to the next, but definitely from the LM317 to the LM337. For the most part, the relationship between
Iadj is linear (from experience), but things change a little when you start to draw significant current in the load - hence:
High Current Regulation:
R3-5 (circled in blue) do the donkey work when it comes to the current. However, this relies on careful choice of values for the resistors. Note: "2R" and "R" do not mean "2 Ohm" and "1 Ohm" respectively; they refer to one being double the resistance of the other. This topic is covered in several versions of the datasheets for these regulators and online, so I shall not reiterate it here. Ultimately the goal is to divert as much current away from the regulator as possible and force it through as many transistors as you need, but you will have to determine the best values for your own needs.
Do not attempt to draw too much current at lower voltages - this means much higher power dissipation from the ICs and much higher temperatures. If
+VDC is 18V,
+V_out is 3.3V, and
+Iout is 3Amps, you'll have 44 Watts+ being turned into heat. I believe that pushes a modestly-heatsinked pair of TIP147s to burning point.