TEFL courses - my employer wants me to go to HCMC for one

There are cheap online courses, but those might not be worth the paper they are printed on.
Seems this is one of the things one has to do. Jumping through hoops is not uncommon in my home country either. (Notary service just to get the criminal background verified?! That will be $ 50 at the U.S. embassy alone!  :/  )

As long as it says "no entry" they should just issue it if the request comes with a photocopy of one's passport complete with the Visa page for Vietnam, JMHO).

Where can one get notary service outside the big cities? Going to Hanoi would take hours each way. But local municipalities may have a seal or official looking stamp? What about the Police?

The payment for the EU Police Report was sent from my bank account with my passport number as a reference. Alas, that won't be enough. I do hat spending > $ 100 for such a thing!

In my opinion is best to get the Certificate from back in the state.
I also believe that you will save around 400-600 Dollars.  A course here in VIetnam is around 1500.00 which is a ridiculous price. 
Good Luck

I'd tell them "Okay!" and never look back, if I were having as many problems with them as you are with that outfit.