The expression: "His Own Man" is a campaign slogan to tell the public that Heyward makes his own decisions and takes orders from noone: no union bosses, corporations, special interests, etc. It's complete nonsense, but that's what he's trying to convey. In reality Harry made every decision for Heyward.
I think Heyward telling Linda to go to his office is to show what a serial cheater he was.
I like how you notice the different actors playing different roles. I'm going to have to rewatch the episode now looking for the seamstress, etc.