We chartered a boat with Dive With Martin for $400 when it was me, my wife, and 2 daughters 3 years ago. I imagine any dive op will charter a boat. Another option might be to go on a regular 6 pack boat and hire a private divemaster. I believe the going rate is $50 so financially your about at the same price anyway. Dive With Martin will do a 3 day trip for about 65 a dive, everyone else I have priced is at the 80-85 per dive(not including gear, big tanks, or Nitrox) Aldora is at 92 I think. I would shoot an email to Aldora, Blue XTSea, Dive With Martin, Tres Pelicanos, Blue Magic, and a few others and see what they can do. My experience is that the competition works in your favor and most ops will work to get your business.
I understand wanting to have your own boat. My daughters first dives after certification were in Cozumel and the extra attention for just them, along with not having to worry about messing up someone else's dives if they had a problem, was well worth the extra money we spent. The boat also went out on our schedule, surface interval length was up to us, and dive site selection was up to us within our skill levels. A chartered boat made for a great first dive experience for my daughters. On the more experienced side, if your hearts were set on more advanced dives and could not go because of new divers on the boat....I get that too. Barracuda may be my new favorite dive and I would be less than happy if I went to Coz and did not get to do it at least once.
Safe travels, Happy New Year!
Jay