When a pronoun is part of a compound structure, put it in the same case you would use if the pronoun were alone.

Eliminating the other part of the compound, José and, leaves Come to the park with me.

Pronoun case in a compound appositive is determined by the word the appositive renames. If the word functions as a subject or subject complement, the pronoun should be subjective; if it functions as an object, the pronoun should be objective.

Panelists is the subject of the sentence, so the pronoun in the appositive Tony and I should be in the subjective case.