Guessing the definite purpose is not a constant load? Maybe a `fridge, etc?
A non-constant load or a load under the peak power input will still need the dump controller and load.
Kind of sounds like you are looking for the antique `bang-bang' controller, maybe set a bit lower for the high trigger point. When the battery reaches the high trigger point, the relay would send power to the definite purpose device until the batteries are down to the low trigger point.
The load specifics need to be known to get much good information.
G-