This represents 100% of my knowledge of DME over-ride!
Not surprisingly, modern DME ground stations which have reached maximum capacity of interrogations, intelligently refuse to accept any extra aircraft interrogations. Which aircraft get excluded? The ones with the weakest (therefore most distant) signals.
So even if you do have DME over-ride selected, I'm guessing that the DME stations around Heathrow and Chicago probably aren't going to talk to you when you're 300nm away...