0V LDO Adjustable Regulator
The LT3083 is a good device and your limitations on drop-out can be improved by considering the following: -



As can be seen, the drop-out at 3A load is just a bit over 300mV but at 1.5A it is about 170mV. Given that devices can be paralleled (diagram on right), maybe you should reconsider this device. Also note the larger words at the bottom - to truly get down to 0V you will need to generate a small negative voltage that is still "removing" 1mA from the device.