Yup, you are wrong. November to mid-December is part of high season. It's not as crowded as the second half of December, but there will be plenty of other visitors.

You certainly don't need to go with a tour group, but you will want to do at least some pre-booking of accommodations. I'm sure your hotels can refer you to reputable drivers.

Hopefully Mohammed will see your question and respond. he lives in Colombo so can give you more info.

i'm also thinking that during your first period you will receive tons of info from people you meet as to where to stay and how to get there..

We were in SL for a month in Feb 2011, which, i suppose, is considered high season. However, we were affected by the floods for a week or two of our time there and had to move hotels a couple of times and it was very difficult to find any where even using a tour company. Anywhere near Yala was completely impossible.

We would normally travel completely independently, making it up as we go along but for SL we did engage a tour operator for approx half the time as it was both easier and not much more expensive than DIY.
With 1 1/2 months there at the start, I am sure you will be able to source a decent driver who can both get you around and help with arranging accomodation.

As for public transport, I always try to use it wherever I can around the world but in SL I made and exception based on the state of many of the buses, the driving standards of the bus drivers and, the number of buses I saw crashed or broken down (& believe me, I am not a nervous traveller by any means!).

Most hotels and guset house have separate accomodation for drivers ans it is often included in the daily rate you would pay. Hiring a driver is not as expensive as you would imagine and, get a good one and he will improve your trip immensely. Two weeks into our trip and we ot our driver to drop us off at Goyambokka on the south coast where we got tuk tuks from town to town until we got to Galle when we got a car to take us back to Negombo.

Another way to go would be to use the train system as much as you can as some of the rides are amongst the most spectacular anywhere in the world. Tickets are dirt cheap, particualrly for second class. It is easy to get around parts of the country by train, particualarly the tea country, Kandy etc. The availability of taxis can be a bit hit and miss at the stations as I recall. Glad to see you have included Adam's Peak - a truly magical place!