Projects that acually do something are the most fun. So lets go for it.
You'r the battery guy so what do you think about powering it off of the battery under test? At 6 volts the circuit will probably draw about .2 amps. Most of that driving the relay. We could, I supose, reduce this to .02 or 03 amps by using a solid state switch. Probably not much more complicated and we could probably get that much from a "dead" battery. Short of that we could do the low power version (solid state switch) and use AA batteries to power it.
We will have spare comparators so a full charge indicator should be easy enough.
Also pretty easy to do a test in process indicator.
It will probably keep you busy figuring out how to package the whole thing.
One other thing I worry about is do we need to protect against hooking the battery up backwards?
If you don't mind we can get the parts from Mouser. They have a bill of material program so we can all see the datasheets and when you are ready to buy you just push the button.
Have you made a pcb before?