Some electric screwdrivers use only one diode to rectify AC current from a wall mount transformer for recharging the screwdriver's internal batteries. It is not real efficient because it wastes a good portion of the AC sine wave cycle, but it is cheap and it works. It would provide choppy current, which is better for battery charging, anyway. The four diode rectifier mentioned is called a bridge rectifier, in case anyone is unfamiliar with them and wants to search for an explanation on the Internet that would allow building one.

An electronics book I have says batteries in parallel with another DC source have the effect of regulating the voltage. I have not tried it, but it sounds like it would work.

I am not sure about how well a low pass RC filter would work to reduce spikes. It seems the spikes would be voltage spikes, not frequency spikes. RC filters usually reduce frequency spikes. You could always try it. All engineering principles were developed by trial and error at some point.