It's dangerous for me to judge since I'm not in your office, but reading the thread gives me a sense of the tone of the discussions (and I reserve the right to wrong on this, as always...apologies if so):
Hard line, black & white, technical/professional, via impersonal email:
"Bill. You need to send another invoice the Z Company. This time, it needs to be sent to their SanFran office, not the Michigan office. I told you this eight weeks ago, and I've got a stack of emails proving I told you to do this. This is YOUR responsibility, not mine, and you need to do this. This is critical and needs to get done now."
Softer approach, with extra effort to do face to face in his office door:
"Hey, Bill, need a favor. Is there any way we could get another invoice to Z Company? It seems that one was sent a few weeks ago, but mistakenly was sent to the wrong office in Michigan. They're ready to pay RIGHT NOW, but for some reason the money guy is in SanFran. Sheesh, it's never easy, is it? What do you say?"
I've had to school my lovely wife on such matters before. Unfortunatley, it is CULTURAL thing about which little will change: many males don't react well to assertive females, no matter how professional they are. The character "Alice" in the Dilbert strip is a perfect example of this phenomenon.
Yeah. They're dysfunctional idiots who should be run over with an old truck and stabbed with wooden stakes. So you need to help them be better dysfunctional idiots.
The bigger question: why are you wasting your time there, and getting all aggravated in the bargain? It seems like you have your documetation to prove (to your next client/employer/self) that your reputation for professional behavior is intact. That's all that matters, what those chowderheads THINK means nothing, absolutely nothing. Drop 'em, move on, live your life.
TygerDawg
Blue Technik LLC
Virtuoso Robotics Engineering