If you haven't been to HK before and you don't know your way around and you don't speak Cantonese then I'm not at all sure that just trying to haggle a day rate with a taxi or minivan driver is going to give you what you want.

There are links from the Discover Hong Kong (Tourist Authority) site to various tours that are available, and while this may not be exactly what you want either it does give you lots of contact details for different tour companies who should be able to customise something for you.

One of the biggest operators is Grayline, and they have guided limo tours with English speaking drivers available. An 8 hour tour (assuming your 11 hours is arrival to departure) in a nice vehicle would cost $5200 plus admission fees, parking and tolls according to their site here.

This is obviously a lot more than a taxi would cost (probably no more than $1000) but it will be far more comfortable (5 in a taxi is possible, but hardly comfortable for 8 hours), and far more effective in getting around and understanding what you are seeing. For a one-time trip with limited time I really think a professional tour guide would be far better than some random taxi driver with at best dodgy English.

(I haven't actually ever used Grayline and I'm not connected with them - they are just a well-known name)