Likewise is Canada, I got a list of what documents I needed, ordered what I didn't have and when the package was complete I sent them all to my lawyer in the DR to be checked and translated. The lawyer sent them to the DR Embassy in Ottawa, I went in and paid the fees and within two weeks the residency visa was approved.
I waited about a month before submitting the passports for the visa stamp so as to maximize the available validity period. I don't know if any "back & forth" went on between the lawyer and the embassy during the processing period but I wouldn't be surprised if the lawyer kept the visa clerk moving in the right direction with all due haste. Give a Dominican functionary a desk drawer and lots of processes can come to a grinding halt - out of sight, out of mind...