I received the record only four days later. Talk about a quick response! Unfortunately, it wasn't what I had hoped for. It turns out it was a family bible, but it was for one of Peter and Elizabeth's children. The only reason that it even had that couples name was because, for some reason beyond comprehension, the folks who transcribed the bible decided to supplement the information with more "facts" from a published family history. Based on the bible as published, this transcription is actually useless to anyone, since you can't tell where the bible ends and the extra information begins. Sigh. I guess they were trying to be helpful?
Regardless of how this request turned out, I still feel like the GRC is a great resource. It's an index, so it's something of a game of chance. There are some Daughters who, through their positions in the society or through their hard work, have earned access to view digital copies of these records. Going forward, I might reach out to them before ordering a record.