But suppose we abandon the beliefs/values separation: what properties do we have left? Is the concept "mind without a beliefs/values separation" Simply the concept "thing"?

An agent using UDT doesn't necessarily have a beliefs/values separation, but still has the properties of preferences and decision making. Or at least, it only has beliefs about mathematical facts, not about empirical facts. Maybe I should have made it clear that I was mainly talking about empirical beliefs in the post.