Hello all who replied and future US military train travelers stationed overseas in Europe/UK!
I got an official reply back from the ticketing agents and, sadly, it is a no go. I will have to purchase another set of tickets as Eurorail tickets. Here is a copy of the email reply:
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Unfortunately, military orders are not considered as proof of residency.
To be eligible for an Interrail Pass with the UK as your stated residency, you require a valid ID which could be: TIER 1,2,3,4 visa / Ancestry visa / Certificate of Right of Abode / BRD Biometric Residence Permit. If you do obtain either of the mentioned documents, you are eligible for an Interrail Pass.
However, if you are unable to provide any of these documents, you can purchase an Eurail Pass. Please kindly note, with an Eurail Pass you are not restricted in your travels. Whereas, with an Interrail Global Pass, you can only use the Pass in your own country during two travel days of your choice for one outbound trip (leaving your own country) and one inbound trip (entering your own country).
You can take as many trains as necessary to complete these journeys, but you are not allowed to make any extra trips within your own country. You can also use them in the order you prefer (that is, you may use the inbound trip before using the outbound one if that better suits your travel plans). You can read this page for more details.
We hope to have informed you sufficiently, and should you have additional questions, please feel free to reach out to us once more. We will be happy to further assist.
Best regards,
Zalikha
Customer service team
Eurail BV