I have to agree that becoming a DM won't necessarily make you the most experienced person in the group but it can! It is true that the bulk of the DM course, at least the PADI version, focuses on good leadership skills and what makes a "professional" but, with the help of a good instructor, you can also build your dive skills and problem-solving skills. In fact, if more dive experience is what you seek through the DM course, I would specifically search for an lds/instructor who can accommodate this desire. For example, work with a lds or instructor who will have you fulfill the "intern" portion of the DM course so that you get real-world, hands-on training with real divers in real dive situations. Go on as many extra dives as you can, to build your own personal dive history but also to work with as many divers/dive experiences as possible.
Also, you'll hopefully be assisting with OW classes where you'll most likely get to see divers in true panic situations as they attempt to peform their basic scuba skills. This experience is invaluable training. Panic doesn't only happen in a pool or confined water setting, it happens in the ocean all the time - and a lot of times it happens with experienced, certified divers such as the group with which you will be doing a lot of diving! Having gone through a DM course and assisted in previous panic situations will help you to identify potential problems, hopefully nip them in the bud before they actually happen, or help you to successfully/safely handle them if/when they do occur.
So, I vote for the DM class, as long as you make your expectations to your instructor & local dive shop clear.
One final opinion (thanks for indulging me)...I would not make you the one responsible for renting/handling all the gear. Each diver should always be responsible for their gear at all times. If they don't know what they are doing, they shouldn't be diving, IMHO.