Some linear regulators, such as the LT3081, require a minimum load current for regulation (5mA worst-case for the LT3081). Since it can be adjusted to 0V, using a resistor for this purpose can require a low resistance resistor which can dissipate significant power if the regulator output is adjusted to a high voltage. My suggestion is to use a two NPN transistor current mirror to provide the 5mA.. That will allow adjustment to 0V without dissipating significant power at high output voltages.
Does that seem like a good idea?
Your idea is good and it will allow you to adjust VOUT to about 50mV above 0V. If you want to adjust VOUT all the way down to 0V, it is necessary to create a negative voltage rail but your current mirror idea will be useful in that case as well. Usually some type of charge pump is used to create the negative rail for this purpose.