I think your volt meter is over reading by about 0.5 of a volt .. taking that off of all your figures and its working just fine .
I assume you have no more alternator light on ?
just for the record then anything below 15 volts is ok .. different battery states and wiring can give different charge rates .. along with how accurate a meter is as well
i would drive it and see how you get on .. any problem with the battery and it will go flat after 3 days or so if not used but that wasn't the original problem so it should be fine .
