I cannot personally speak for the "a few hundred miles", but I have
experienced mountain wave within ten nm of the lee side of the
Appalachians in both North Carolina and Georgia.

Dave Butler wrote:
Here in NC you can get mountain waves a few hundred miles downwind from
the Appalachians, though I've never experienced anything as severe as
the OP describes. I think St Simons is too far south for Appalachian
mountain waves, though.