I can confirm that there is a method to speed things up. We married in Dalaguette, and had to chase up the papers to be sent to Cebu City Hall. From the City Hall we had to pay for the documents to be processed quickly. This was relatively quick, and can be controlled fairly easily by a bit of pressure and expedite fees.

Then the next step is the NSO, and this is done quickly through 'Advance Endorsement'

If the birth/marriage/death occurred within the Philippines, you may file for "advance endorsement" at the Local Civil Registry Office (LCRO) of the city/municipality where the child was born. Advance endorsement means requesting the LCRO to advance ("endorse") a copy of the birth certificate to the National Statistics Office (NSO) ahead of the regular schedule of submission of civil registry documents. The LCRO will charge a fee for this service.
Please ensure that the copy to be forwarded to the NSO is the ORIGINAL COPY for the OFFICE OF THE CIVIL REGISTRAR GENERAL, or the OCRG Copy. Otherwise, you will be issued the NSO Feedback Form containing further instructions.
You may have the document forwarded to the NSO via your preferred local courier service; this will be to your account. Delivery should be addressed to:
MS. LOURDES J. HUFANA
CIVIL REGISTRATION DEPARTMENT
NATIONAL STATISTICS OFFICE
3/F VIBAL BUILDING, EDSA COR. TIMES ST.
QUEZON CITY 1104
Thereafter, you may apply for a copy/copies of the birth certificate through this website. Kindly provide the following information via email at e-census.info@census.gov.ph, or phone at (632) 981-7777/-7778: