You're incorrect on point 2. In many communities, schizoid/schizo does refer in a derogatory/shorthand manner to schizophrenia and many more people are familiar

You're incorrect on point 2. In many communities, schizoid/schizo does refer in a derogatory/shorthand manner to schizophrenia and many more people are familiar with schizophrenia than schizoid disorder, so that is more likely to be the immediate assumption.