According to manual this is how I pass extra arguments to Sendmail:

Again, it doesn't say that at all. What it actually says is:

Any remaining arguments will be passed directly into your defined message_modifier

You neither defined a message_modifer, nor would it help if you did.

Unfortunately, no matter how I try that --extra-arg just get lost somewhere in the middle and never reaches Sendmail.pm send function.

Nor should it reach Sendmail's send.

I think mailer_args will do the trick, though.