I think people are missing the plot here a bit with taking trains or overflying the UK and lifting a walk-up fare on an LCC.
I applaud the OP for spending 3 hours on the phone today to try and get this resolved, but no point spending more than the flight's block time getting this resolved.. If Twitter can't do anything, get to the airport quite early and plead a case there for a reroute through ORD.