That 10k resistor feeding current into the BD681... if you can connect it to a voltage higher than Vin, then you can reduce the dropout voltage significantly.
The current limit is very basic, and it necessarily results in a minimum of 0.6 V of dropout. You will need an amplifier to do better.
I'd move the current shunt and limiter to the input side of the pass transistors. Connect the 10k resistor mentioned earlier to Vin (not the output of the current shunt). Then you reduce the dropout a little bit. Refer to my circuit below that I designed a few years ago and is very similar to yours. In my circuit, the extra gain from using two transistors in the current limiter makes it much more accurate/stable than a 1-transistor version. (R3 and R6 are a 1k pot)