Well, I found the source of the problem tonight. It turns out it was the alternator. Fortunately, I had the old one lying around to make comparisons against. I actually installed it a couple of days ago in hopes that it might work but since it had the same symptoms I dismissed it as a possible source. But tonight I took both of them apart and saw the difference. The old one has 2 insulated field connections, each with brushes that contact the armature. The new one, however, has just 1 field and a ground connection, with brushes attached to each. I had my 2 fields connecting to the field and the ground with it grounding to the case. I can't understand why they would configure an alternator this way (grounding one of the brushes), but that is clearly what it is set up to do. I should have noticed the "GRD" stamped on the case next to it, I suppose. Any insight as to what this alternator goes on would be appreciated, as would any recommendations on how I could possibly salvage this alternator.
