An update on this, I called AppleCare and talked to the supervisor. He was concerned when he looked at the old repair and noted that it was "very strange" that the techs did not write down any notes after they looked at my iPad. Further, he was flabbergasted when I told him they sent it back via Fedex. "They don't know the difference between Fedex and UPS?" Eventually he said his software asked for a picture of the device (first time he's seen that), which after I emailed him it, he said he saw the problem then. He did some extra paperwork for a new repair and said he'd make them send me a new one. My old iPad is almost to the repair center and I will get a new one back.
I also asked about "refurbished" replacements. He said that it was generally at least 5 months before they would send those out due to the fact that they have few parts around, but he said I'd be getting a new one anyway so I wouldn't have to worry.
My experience was great, and both the first rep and the super apologized for the long wait because the repair form takes long to do on their end, consulting with the repair center and such. (The call was an hour and a half long).