The crazy thing is, as expensive as this sounds, this is actually well within reach. The Moorings (www.moorings.com) offers a variety of yachting experiences, ranging from "learning to sail" trips to the fully staffed yacht charters. While I haven't exactly figured out what the appropriate level of charter would be for me and my family, my initial take was that I could get a week long powerboat yacht charter with staff for only around $5,000. That's total, mind you, so significantly less than my first pick (the Orient Express) which ran around $4,000 per person.
Yeah, this is pretty close to what I'm imagining.
While I probably still have to do a little research on this one, it does seem surprisingly affordable, especially for a family of four, although destination and craft type may create some different pricing points. That said, I might have to look into this as an option in the nearer future than I had originally thought.
What I would like to know is other people's experience with this sort of thing. If anyone out there has chartered a boat or spent any time sailing (or learning to sail), I'd be curious to hear your thoughts.