How would you design a variable current divider for non linear loads?
In this case, the simplest answer is: a rheostat.







simulate this circuit &ndash; Schematic created using CircuitLab

with a starting value as shown will provide operation, although the resistance will take a bit of tweaking depending on the exact extinction ratio you want. A smaller resistance will probably work just fine.

A wiper current of several hundred mA is too much for standard pots, but rheostats are designed for higher currents.

The circuit takes advantage of the exponential voltage/current relationship for LEDs, and in effect encourages one string to hog the source current while the other is starved.

If the circuit as shown is too sensitive, small resistors (~0.1 to 0.5 ohm, I guesstimate) can be inserted into each string.

Because the resistors involved are small I'd estimate pretty good (>90%) efficiency.