"I will try to express myself in some mode of life or art as freely as I can and as wholly as I can, using for my defense the only arms I allow myself to use -- silence, exile, and cunning." -- James Joyce
I think Walter Block is just a lost cause at this point. He has sailed beyond the event horizon of insanity.
Block's own view doesn't fare much better than Rothbard's concerning the "right to abandon." What Block does (according to his 2004 paper) is merely narrow down the cases in which a parent can starve their child to death "justly" (in accordance with libertarianism). The parent would have to make known the fact they were giving up their ownership of the child and would not legitimately be able to use their property (such as the boundaries of their home) to block a path to reaching the child. However, if no adult was willing to take in the child, for whatever reason (lack of information, immoral character, impracticality, etc.), then we are still left with the absurd consequence of the child's death.