We do business with Shore Trips and they have also booked tens of thousands of excursions for clients over many years and have NEVER had anyone miss the ship. Should that ever happen, they have insurance to take care of the client and getting them to the next port of call. But these companies never have any problems - it's those out doing their own thing that miss ships, not organized shore excursion companies.
As for the time, you should be fine. All of the major independent shore excursion companies know what time the ship leaves and what time you have to be back. Cruise lines like to have everyone on the ship 30 minutes prior to departure. So these companies will have you back in plenty of time and there's no need to worry.
So, I would have absolutely no problem with booking an excursion like the one you've chosen.
Besides, St. Lucia is one of the most beautiful islands in the Caribbean and really demands exploration. And the good thing about the independent companies is that they are usually cheaper, usually much nicer, and almost always alot less crowded.