Just get the clearance from the port of departure and be sure it lists all the crew and passengers. That is all the proof you need. The coast guard knows that departures and arrivals are taken very seriously by the Dominican port authorities. For example, US Customs in Puerto Rico normally doesn't give departure clearances to departing vessels. But they will give you one if going to the DR because they know the Dominican port authorities want to see it.
I've crossed the Mona in a sailboat more than 10 times and was only boarded once. And that was very close to
PR. Of course, with the current security concerns they may be boarding more often. But if you have the departure clearance from the north coast port they will know you are legitimate.
If you are taking Dominicans on a sailing yacht that will be traveling in the Mona Passage, you can be very sure that the Dominican port authorities are going to take great interest in what you are doing and who you are proposing to take. In fact, they may not let you take some or all of the Dominicans you propose to give a ride to. You can also bet that if they do allow some or all of the Dominicans to accompany you, that they are going to notify the port commander of the arrival port that you are enroute. If you don't arrive when they think you should, somebody will likely come looking for you. They may even notify the USCG to keep their eye on you to be sure you aren't headed for
PR.
If I was worried about calling attention to myself, I certainly wouldn't invite a group of Dominicans to make the passage with me from the north to the south coast.