Just use a current-mode converter like the HV9910 or the ZXLD1360.
These don't generate any significant heat, work with smaller power supplies, and regulate the current very accurately.
Otherwise, as you drop the supply voltage near the LED's forward voltage and lower the ballast resistance, the ballasting becomes less reliable. For one, the forward voltage of the device is not known exactly. Second, the forward voltage drops as it warms up which would increase the current when the voltage across the ballast resistor is low.