I'm thinking that car rental quote has to be some kind of a typo, as you should pay about 1/3 of that rate in October. Regardless, rent the car. If you're making that many trips, it will cost you much more for taxis and it will be extremely inconvenient to wait for someone to show up to pick you up that many times.

If you are determined to not rent a car for other reasons, suggest you contact TTOL sponsor Wilfred Brooks and arrange to have him do all your transport. At least then you won't go crazy sitting around waiting for taxis to come.