This strikes me as being roughly similar to peoples' opinions of the value of having children who outlive them. As the last paragraph of the OP points out, it doesn't really matter if it's a copy of me or not, just that it's a new person whose basic moral motivations I support, but whom I cannot interact with

Having their child hold to moral motivations they agree with is a major goal of most parents. Having their child outlive one them is another (assuming they don't predict a major advance in lifespan-extending technology soon), and that's where the non-interactivity comes in.

The post-death value of the child's existence is their total value minus the value of the experiences I share with that child, or more generally the effects of the child's existence that I can interact with.

In this sense, the question of the poll can (I think) be rephrased as: what, to you, would the post-your-death value of a child that you raise well be?