If the camera is not moving, and if only a certain percent of the image is animated, you can render only that portion and maybe save some time.
Later you can even add a slight 2d general movement in after effects or some freeware video editor.
EDIT :
You can even animate the "crop" or the rendering portion selection - so it will follow the area of the screen where the animation happens. An animation can start as a very small portion of the screen - so the rendering will be very fast, and it can increase in time.
But the final image output will be the final complete resolution, so it will be easy to composite on top of the background. Not sure how clear is what I just said :)
Also if you would have at least a second computer, you can render on one and continue to work on the second one.