My wife and I have used both approaches in past visits to St. Martin -- renting a car or just using taxis during our stay. Both methods work, and the pros and cons you outlined above are well thought out. I don't have any past experience with Mr. Brooks (I don't think), but if Carol recommends him I would trust that recommendation. Another 'pro' for using taxis is driving at night. During the day I can dive anywhere, but at night it's so much easier having someone do the driving for you. Things sometimes just look different at night (though it's hard to truly get lost on St. Martin). The only additional suggestion I can provide would include trying to establish some type of schedule for your visit, and arranging your taxi rides accordingly. In some places on the island it seems like taxis are everywhere. In some other locations it can be a challenge to find one. For example, if you plan to visit Friar's Bay Beach for the day (which is somewhat remote) having a set pick-up and return time in advance can really help.
Good luck with your upcoming visit.