If you are careful enough you can make an LM317 go to 0V too. You use this chip and you create a -1.25V reference. Now you put any voltage in the ADJ pin of the LM317. If you bring it down to -1.25V the output will be 0V, so theres a 1.25V offset of course. You have to use a current source like you are doing right now as well, I am guessing. If you are going to use a DAC to connect to the ADJ pin, you have to use the -1.25V as the negative reference. In fact you may have to make the -1.25V rail your digital "ground" (I think it's more of a common terminal) and make the positive supply 3.75V if you are using 5V logic.