After googling for longer than I care to admit (maybe I'm just using the wrong search terms) it seems there doesn't exist a repository of sample EDI files anywhere. For such a pervasive data exchange format, I'm surprised. Even though there may be variations from company to company, I would still think the industry would benefit from having a repository like this.
Am I embarrassingly missing something?
You hit the nail on the head: "there may be variations from company to company". You didn't specify standard. If you're looking for EDIFACT, you're in luck! They are published freely. If you're looking for ANSI X12, well that standard library is published, but it'll cost ya. Your partners can usually send you sample files as part of the implementation. X12 handles a lot of vertical industries. Some subgroups might publish their own X12 specification (HDA for the pharmaceutical industry for the ASN, as an example).
Companies bastardize the standard all the time to suit their needs.
Feel free to download and check out this tool: https://www.liaison.com/products/integrate/edi-notepad/edi-dictionary-viewer/