You could go a little old school and use a light bulb and an ignition switch similar to your car in place of the resistor, regulator, and possibly the relay. The lightbulb would be a standard 120V incandescent lamp. (Thinking oven/refrigerator lamp) Dynamically the lamp would provide a HIGHER resistance when it is lit (charging) and a LOWER resistance as it goes out (charged). Initially there would be a LOW resistance spike, but that's what lamps do from a cold start.
The idea with the ignition switch it has TWO positions you need to use ... One when you initially stick the key in and partially turn it FORWARD. This would be the "charging" period through the LAMP. The other (momentary) STARTING position would engage a RELAY or if you wanted to eliminate the relay, turning the key BACK (as you would normally do in a car if you just wanted to listen to the radio without the Engine running) ... this position would simply short out the LAMP.
Note: In the BACK option make sure you check the current capability of the ignition switch.