UPDATE
The British Airways "computer" shows LEX/SDF as >350 miles from CVG. He spelled the airport code back to me phonetically and had it correct. He said he and his boss looked it up online and the boss was able to make an exception due to their system clearly being incorrect.
I was then able to give him flight numbers based on what I was seeing on Google Flights. Knowing BA is part of Oneworld, I chose that network and added a minimum of 2-hour layover (to add delay cushion) and sorted by Emissions. He was able to get us on the top result: LEX-ORD AA 3215; ORD-LHR AA 98. LEX is much closer to our house, but BA 120 is the only direct flight to Europe in my area, hence why we were originally making the drive to CVG.
Success!