Took the '67 289 Out for a Drive: New Battery Died

Update.

The alternator was bad. So I just installed a new one. New wiring harness to the alternator as well. Still same result: no charging of the battery. Don't know how to find this problem with a volt meter - what to check to narrow this issue down???
 
I am in agreement with what the others have said about checking the grounds since you painted the engine compartment. What I would do is remove the mentioned grounds and remove the paint behind them and reinstall. Here is something I did on mine. I used small bolts with star washers and nuts on the back to get a better ground.
 
not to go off topic, but from Ohio to NJ on just the battery? that would have to be during the daylight without a single stop for gas....even on my little 4 cylinders I was never able to drive for more than hour on battery power. If I turned the car off after about 1/2 hour it wouldn't start back up.

It was daytime and it was a 4-cylinder, and we did stop for gas once and didn't shut it off.

Sure, this was ideal conditions for extended running, but his original statement:

Car didn't seem to overheat, but after about 45 min of running around in traffic, it just slowly died while idling at the local burger joint

Even if his alternator is stone-dead, that's not much time. HiPo pulleys only "stall" the alternator at idle, so unless he was crawling around town at 700 rpm, his "New 60A chrome Powermaster Alternator", more powerful than anything the factory had at the time, should have pumped out some juice at some point.

Unless, of course, he has the sound system from hell… View attachment 246552