I just had my car shipped to PR last week...
I received several quotes and puertoricocartransport.com was the best price.
It went fairly smooth. It was $2375 from San Diego > Jacksonville, FL > PR.
It's about $1200 if you can otherwise get the car to the port in Jacksonville.
It took about 16 days in my case from when it was picked up to when it arrived in PR.
Make sure you are aware of the excise tax cost - you will need to pay it when you pick up your car. Hope that helps