just as a follow-up, I did sign up for the PADI course. it was a great course, and there was an (otherwise unadvertised?) option to "upgrade" the cert for $100 to a full-blown open water cert with another day of classroom training and pool dives. This "upgrade" allowed us to check off all additional requirements except for two additional instructional dives (out of 4 total) - so I will need to do two more dives at home.
I was told on the western carribean itinerary, they are able to complete those two additional dives and you can get the fll-blown open water PADI cert since it has additional time in port (1 additional stop?), but I'd expect it would be more than $100.
The course did take a lot more time than I anticipated, but in my situation where I am strapped for time at home it was worth doing onboard.
Hope this helps!