Ammeter is making me nervous

Well the high voltage out of the alternator and the large voltage drops to the battery are problems. The high alternator output may have cooked your old battery and may be causing the large + ammeter readings. Have the high ammeter readings and large voltage drops from alternator to battery settled down at all with the new battery? I ask, in case the old battery had a partially shorted cell that was causing a high current draw. I would put the new battery on a charger overnight, disconnect the charger the next AM and let the battery rest for an hour, and check the battery voltage to see if it shows 12.6-12.7 v after a good charge and resting. This let's you know if the the battery is solid and not internally shorted. It is important to do this in this sequence, even with a new battery, with your high current draw symptoms. (BTW, I have had 2 bad brand new batteries in a row one time so take nothing for granted!)

Start with all the tips written on how to test for voltage drops. But it seems likely that you have one of a few issues. (And this is not new, just saying it again....):
1. You have some bad voltage drops in the main output wire from the alternator, through the firewall, and to the welded splice, then on to the regulator via the red wire to the ignition switch and then on the dark blue wire that goes to the ballast and VR. (Would not explain the heavy current draw though).
2. The ground leads are bad somewhere. (Would not explain the heavy current draw though).
3. There is some heavy current draw in the battery side of the ammeter; there is not much there except the ammeter itself, the harness, the firewall connector, the fusible link, the starter relay, the big lead to the starter, and the battery.

Not sure what to say about your observation #3; how hot is 'hot'? It could be a sign of the heavy current draw or just engine heat.