If you are seeing AC voltage at the battery, the rectifier has at least one shorted junction, letting current flow both directions. The battery is effectively the voltage regulator in that charging system (just like on the singles), without a good battery, you will blow bulbs. The 350 was the only BS with an effective voltage regulator.
Search the forum for rectifier replacement, you'll find suggestions on using an aftermarket three phase bridge rectifier. Don't bother looking for a good used OEM one, they are very likely bad.