We did a trip like you are wanting to do a few years ago. We stayed at Lake Rousseau RV Resort (nice people, mainly permanent sites). It was kind of a middle ground for where we wanted to paddle.
Check out Rainbow River Canoe and Kayak, they offer a shuttle on Rainbow River. It is a great 5 mile float trip. The water is incredible, with tons of wildlife. However due to a Ram, manatees are not on the river. Google pictures from Rainbow River, it is amazing. It is in Dunnellon FL. Rainbow Springs State Park s at the head spring, but it is hard to find a vacancy.
Crystal River has tons of manatees year round, and is not to far away. When we went there was tons of wind and had the water murky, and the waves out in the main river were to rough, we did see lots of manatee noses pop up to get air. We are wanting to go back again and hoping for better weather.
It is also about an hour from Manatee Springs State Park, it is really a pretty place. Tons of wildlife, manatees, gators deer etc.
It is an amazing area, We did a week long trip, and split it between Disney and kayaking. On the way home my kids said they wished we had spent the whole week paddling and skipped Disney.