Christianity has its own justice problems: original sin, bearing consequences of Adam’s act that no one remembers or chose, and eternal punishment for finite sins. Shouldn’t the memory objection to karma expect to come back?

It should, and the symmetry must be engaged. On original sin, the Christian reply is that inherited consequence (mortality, a disordered nature) is not the same as inherited guilt, and many Christian traditions deny inherited guilt; but some affirm it, and for them the memory objection has force. On hell, this site does not offer a full treatment, and the objection stands until it does. Every account of suffering across generations faces a justice question. The Christian answer locates ultimate justice in a personal judge who knows each case rather than in an impersonal law, and whether that is better is for you to weigh, with the same probe applied to both sides. Edwards’s critique has also been answered at length by philosophers sympathetic to reincarnation, Robert Almeder among them, and that reply deserves a reading.