I had a similar situation a few years back w/ my '67 b-body 440. I had purchased a cheap voltage regulator, and it went bad. Noticed on my voltmeter gauge that as I was driving the voltage started creeping up-14,15,16. Somebody had advised me that the voltage reg was bad. Went to NAPA and purchased a life time warranty VR; was kind of pricey. Problem went away; haven't had any overcharging issues since then. Can't speak about your battery being the problem. Maybe somebody on Moparts w/ more knowledge than I can address that issue.