I have a character with a short tail. It seems (to a noob) the solution would be to use Region or Manual binding for the tail and Flexi binding for the body for reasons that should be clear form the image below. As a noob I don't know if there is a way to do this or if I need a totally different approach.
There's no need of several bone layers. Just keep everything inside one bone layer, it's cleaner and easier to animate.
Now, to solve your problem: Select the Tail layer and then select its bone. Now go to the Bone menu and "Use selected bones for Flexi-Binding". The tail layer will be moved only by the tail bone.
Repeat the same process with the other layers. You can select more than one bone for each layer. Also, you can select several layers and bones and apply the "Use selected bones..." for all them at once.