Well, I suppose it's time for an update. School picked up, and the weather was particularly inhospitable, so I was in no hurry to finish this damned project.
Anyway, I was having two issues: power to the unit was siphoning power from the dash, and no sound. I tried reaching out to a business in town that installed car stereos, and they were ABSOLUTELY no help. They obviously Googled less than I did, and told me that I need the most expensive Metra kit to keep the DIC. I told them I don't care about the DIC, and then I got no reply.
For the no sound issue, it seemed like a harness issue. I was not about to pay more for the harness than I did the stereo, so I threw up a hail mary on a standard harness on Amazon for a few bucks. It came in and sat for a few weeks while I finished the work I had to do. I finally got some time, so I got around to installing it.
The result: success. Turns out the initial harness had been bad; I don't know if it was poor build quality or what, but it was the cause of all problems. Hooked the new harness up, turned the car on, got sound and consistent power everywhere. Drove around the block, everything still worked. Threw the car back together (finally) and it's still humming a few days later.
What a total nightmare. Thanks to everyone who helped along the way. I'm in no hurry to do this again.