I have some other suggested routes if you want to continue pressuring about resolving your case. I think you should use your status as a tourist who experienced such a big theft to your advantage, and take it up with POLITUR and the Ministry of Tourism. They could turn the heat up on Caribe Tours. Even if your stuff doesn't turn up, you could get reimbursed and maybe they will take your case and use it to force Caribe Tours to better protect passengers in the future.
Here are their websites (in Spanish):
Secretaría de Estado de Turismo - Contacto
Policía Turística - Contacto
There is also another website, (in Spanish), that is used to denounce poor service and such events by any business. Sometimes the businesses contact the site owners to get in contact with the person who posted the complaint, because once it is on there it's for all to see...bad press for them.
QUÉJESE.com.do | El portal de quejas y servicio al cliente de la República Dominicana
So my advice would be to write up what happened in a Word document, like specific details (dates, places, times) about exactly what happened, what the response was, and what you want to result. You could also throw in how you may not return to the DR because of this and would hate to have to advise all of your friends to do the same, because you liked your visit otherwise. Then copy/paste the same things on those websites and see if anything happens.
Don't feel bad or take it personal that your luggage was stolen. Yes, there are precautions, but it doesn't always matter. Sometimes, wherever you are in the world, your luck just runs out. Thefts and burglaries are on the rise in the country overall from my perception, so try to also see yourself as a part of a larger trend.