Don't be discouraged.You know the game plan. What you need done calls for patience, even in a wonderful country like Canada.
RAHS does nothing w/o an ANTHEKA (Privacy Release) and yes, if you submit an inquiry w/o it they will ignore you.Contact your nearest Ukrainian Embassy or Consulate and ask them how you need to proceed.As per Intl Law you normally (for records over 100 yrs) do not need a Privacy Release, but given the holding back of documents, my guess is that there may very well be this requirement in this case. It is a source of income for the archives, so they make up stupid rules in order to be able to collect that income.
Even if you were to hire a local pro, you would need to provide Power of Attorney.
One way or another you will be paying 75USD-100USD for that birth certificate, so you might as well do it yourself, but do go thru the Embassy or Consulate and again, be prepared to be patient.