You may have to lie a little
My wife and I are trying to get our residency too. She just went to get our (and our kid's) BCs stamped this week.
The screener there asked why we needed them stamped and my wife told the truth (heaven forbid). Well, they told her that they can only stamp the BCs if they are needed outside of the country. They will not stamp them for purposes of obtaining residency in the DR. Unbelievable!!
Anyway, she made a big stink about it and they would not budge. So, now I have to go in and make up some story that will enable me to have them stamp the BCs.
Their suggestion to her was to fly to Miami and get them stamped.
Anyway, I suggest you not tell them that you are applying for residency. It may make it harder for you.
Good luck!