Electrical Short - What Just Happened?!

Following up with some good news. I've been driving the car for the last week without any troubles, and wanted to give it some time before I reported back. Here's what I ended up testing & doing based on 67dart273's advice upthread:

Battery off: 12.X
Starter relay: 12.X
Starter: 12.X

Yet getting the car to crank was consistently the problem because I had no electric whatsoever. The only thing that would bring back the electrical was disconnecting the battery cables and reseating them. Every single time.

Using that as a clue, I inspected the cables more carefully. Both clamps were a little loose and had some play. I took them apart, sanded/brushed the wires, scraped away corrosion, and even sanded the ground to the engine block. I reassembled everything tightly, and it's started every single time since. On top of it, startup is almost effortless. In the past, if I had let the car sit for a few days, it would take a couple of cranks to get it going. Now, it fires right up.

I appreciate everyone's help. Sincerely.
This is why everybody who wishes to repair their own electrical problems should know how to do a voltage drop test. In your case, if you put a voltmeter on both battery posts and note the reading when somebody turns the ignition key to start. If you then move the positive meter lead to the battery cable and do the same test, it will show less voltage. Or, to put it another way, keep the positive meter lead on the positive battery post and move the negative meter lead to the positive battery cable and read the voltage when cranking the engine. The meter reading will show any lost voltage at that point. Doing this on both the positive and the ground sides of the battery to starter circuit takes all of two minutes. This type of test can be used on any electrical circuit but it must be done with the circuit loaded.