Yes, HIN is the proper term, thanks for the clarification. With the HIN you can go to websites like this one:
https://hindecoder.com/ and get some information on your boat which might include your model number. Your model number can also sometimes be found on your NMMA plate as well. You can also go to your local fraud detection center (call local police station) and they can perform a title and registration search based on the HIN. A lot of times when boats are registered the model information is a part of the registration records. My local fraud unit did mine for $20 bucks and took them 15 minutes. They will not give you personal information, but they will share the details of the registration history including model information if included as part of the boats registration history.
You can also go to Iboats Spec. page and search the details of the 3 models and match the information up against the NMMA plate. I notice there are different weights listed on the spec page for the models you listed...might help narrow it down,
http://boatspecs.iboats.com/
Good luck.