That band is the overlap in any resource valuable to both. How can you be confident that it will be narrow? For instance why couldn't machines put a high value on paperclips relative to organic sentience?

Yes. The answers to those questions fell out once I decomposed the problem to types of mereological nihilism and solipsistic environments.

An empirical, existential grounding that binds agents under the most hostile ontologies is required. You have to start with facts that cannot be coherently denied and on the balance I now suspect there may be only one of those.