I thought I would post back with the results of a few days looking at it with a friend who is also extremely well-versed in Model A.
THE CAR IS RUNNING
We found that internal to the distributor, there was a dead short. It didn't happen all the time, just intermittently. And hence the fuse would then blow and if I was unlucky, some other stuff as well. Flasher relay. Brushes on the horn. Ugh.
Rebuilt the distributor, also got the carb nice and cleaned and adjusted, put a decent timing on and the thing runs like a top.
Have yet to get it on the road because I've only got about 1.5 gallons of gas in it and Texas has gone absolutely nuts with gasoline shortages as a result of Hurricane Harvey fallout. People are nuts, and I'm not going to be one of them sitting in a line for an hour to maybe or maybe not get some gasoline. So the road-test will have to wait.
Wanted to post that the alternator is not the problem. It's putting out plenty of charge, and volts are not excessive.
The ammeter needle now "dances" correctly when starting, and of course indicates charge or discharge. Before the rebuild on the distributor (right before "bang #2") the ammeter barely moved at all.
Now I'm ready for the great gas crisis of 2017 to be over so we can cruise a little!
Thank you for all the suggestions and advice!