Delta finally answered me on Twitter this morning and had this to say:
I have also found the following rules for our Sky Club, "VS Upper Class and VS Flying Club Gold members traveling on a same day VS or DL operated Transatlantic flight between North America and the UK may access Delta Sky Club".
So, it would appear it's the over-water Upper Class ticket and NOT the GM status that gets me access. On Twitter, they weren't sure if the STE+ status would apply.