This tells us that it is not a focus issue but a problem with stability. Long focal length and slow shutter speeds area recipe for soft images. A tripod would keep the camera stable and make it more likely to get sharp shots but it will not help with the motion of the birds.
>> “My shutter speeds are slow…”
Small birds, even when perched, are a very challenging photographic subject. Even when not in-flight they still make very fast movements of their heads and bodies. This requires some fairly fast shutter speeds. I like to be at 1/800s or faster for any small birds. You can shoot slower but you get fewer keepers. Once you get below about 1/180s getting sharp shots is very difficult.
One technique I like for small birds and slow shutter speeds is to put the camera in CH mode and shoot in bursts of 3-4 shots at a time. This increases the likelihood of catching the bird in a truly still moment and getting a clean shot.
Using a shorter TC (TC-14E) will give you one stop more light allowing you to double your shutter speed. It will also help the lens to focus faster. Using the lens without the TC will give you 4x faster shutter speed.
The more that you can fill the frame the better off you will be. If the bird is too far away the camera will have fewer pixels to render the bird so any blur will be exaggerated when you crop and enlarge the bird. I know it is very hard to get closer to the birds but it can be done.