How can you make a statement that doesn't refer to anything that exists? I've done it, and my reasoning process is still intact, and nothing has blown up. Everything seems to be fine. No one has explained to me what isn't fine about this. Since it's intuitive, why would you not want to do it that way?

Clearly, you can make statements about things that don't exist. People do it all the time, and I don't object to it. I enjoy works of fiction, too. But if the aim of our dialogue is true claims about reality, then you've got to talk about things that exist - whether the subject matter is 'oughts' or not.

What one is forced to do by this argument, if one wants to speak only in physical statements, is to say that "should" has a really, really long definition that incorporates all components of human value. When a simple word has a really, really long definition, we should worry that something is up.

I don't see why this needs to be the case. I can stipulate short meanings of 'should' as I use the term. People do this all the time (implicitly, at least) when using hypothetical imperatives.

Also, in general I find myself confused by your way of talking about these things. It's not a language I'm familiar with, so I suspect I'm still not fully understanding you. I'm not sure which of our anticipations differ because of the disagreement you're trying to express.