Having done somewhere around 40 cruises, my husband and I have done a variety of things. In general, here are my thoughts.
Factor #1 is the port itself. There are many ports where we feel safe enough going off on our own. Sometimes, just to walk around, other times, hiring a taxi. But, there are ports that we do not feel entirely safe. For those, we book through the cruise lines. I do feel that they are more strict about who they sub-contract the tours to.
That brings up another question in my mind. Since the cruise ship tours are sub-contracted, why do you not choose to go that route? Just a thought. I don't know your type of business at all.
The second factor for us is the length of time in the port. If it is a relatively short day, we go with the cruise line tours. That is the biggest reason why I hesitate to choose an independent tour. While, as you said, either way, things can go wrong and result in delays, the cruise lines will get you back on board. But, if we have plenty of time in a port, I am much more likely to go with an independent tour company.
A third thing is the reliability of independent companies. I am NOT attacking your company. But, a year or so ago, we intended to book a series of tours through an independent who had tours in 3 of our ports. They never even called us back. I would think that booking more than one tour might motivate someone. We probably just had the bad luck to get one employee who was lazy or not competent.
Last, we have had 2 events where one of us was injured or threatened by independent operators. And, no, I am not overly afraid of things or people. But, both were horrifying incidents. And it can be very difficult to research any company. There is a lot less control in most of these countries than we are accustomed to here in the US. In one case, my husband was injured and the tour company disappeared as soon as it happened. Only the fact that we were near a big hotel who appeared to be promoting the activity and the fact that I was screaming mad got us any help. The other was one where I went alone. It was a tour I had taken through the cruise line a number of times and decided why not do it on my own for 1/2 the price. I would be dead now if I wasn't such an aggressive (and trained) fighter when threatened.
In short, I wish that all independent tour companies were as good as you say you are (and I do believe you), but realistically, they just are not. There is safety in paying that extra amount to book tours through the cruise lines.
Hope that your business goes well. Perhaps someday I will get a chance to check it out for myself, and then write a customer rave review for you on this board.