Although its most likely the battery is on its way out unfortunately you cannot completely write off a RR fault. When testing it the only diodes that can be checked are the rectifiers not the regulators which cant be accessed without dismantling the unit. Even then the diodes that have been checked ok can still give problems under load so its worthwhile putting your multimeter on low range AC volts to see if any ripple is getting through to the battery from the alternator when running.
I have struggled with this problem before and the risk is you put a new battery on and that promptly also fails
