Transporting giant breed dog. And service dog question.

Hi - I can only relate what I have seen and heard, but hope it helps.
If this is a (certified?) service dog, I would call the airline about it - I have heard of people who have taken their service dogs on the plane with them, inside the passenger compartment.  Times may have changed, but it seems worth it to ask.
You mention cargo - are you flying on the same flight as your dog? If so, "cargo" can mean something different, depending on the airline.  Ideally, he would go as "checked baggage" not "cargo" - this saves something (cost? paperwork?) - sorry I don't remember details, but also something worth asking airlines about.
Every person I have read about that brings cats/dogs into CR with them (e.g., same flight), has had no problem collecting them as soon as they land - no overnight worries. 
If you are shipping him (separate flight), then you may have problems. If this is the case, let me know, and I will dig up someone's post about what they went though.
regarding service dogs in Costa Rica - I have seen a couple around town, so I know they exist :-).  Animals are definitely perceived differently here - more as tools than pets.  A service dog would probably be understood more readily than a typical pet.  I do not know how they would be handled on the buses - I have never seen a large dog on a bus, and usually they are not allowed. (I did see someone carrying a small dog on a city bus - once)
You will probably want to practice a short speech in Spanish about a service dog - you will likely use it a lot until you develop "usual haunts."
good luck,
Julie