We sailed on Destiny on June 24, 2007. Thanks to the info here, we had a most enjoyable time. There are three of us, me (46 old dad), wife (uses a mobility scooter) and 14 year old daughter. This was our 4th cruise and second on Carnival.
Embarkation. As good as could be expected. Accessibility issues were small. We bought our rum in the Duty Free shop and had no problem getting it on board. Cheaper than the drinks on board. We were on quickly and luggage came fast, except my suitcase. It arrived about 6:30, not late at all, just later than the rest. As soon as we set sail, it rained. Although I'm sure it didn't rain long, that was our clue to get unpacked and get to bed.
St. Thomas. We went by taxi to Magen's Bay. Beautiful and lots of fish to see without actually snorkeling. The water was as warm and clear as expected. Shopped a bit at the port shops. It was tough having a nice port as the first stop, but St. Thomas is beautiful.