The last trick was:

1. ORD to IAD
2. IAD to LHR
3. LHR to ORD

After typing in the above information using the multicity search, select an itinerary that contained transatlantic segments using BMI codeshare flights. Hit the select button. If the trick worked, you would see a red notice at the top of the next screen "A new lower fare has been found". If it didn't work, you'd get the itinerary you selected with the same fare shown on the previous screen. Sometimes, after failing to get the red notice, hitting the "Back" button on your browser and selecting the same itinerary again would mysteriously give you the lower fare where the first time it didn't.

It's a specific combination of codeshare flights and cities that allowed the trick to work. We'll have to wait and hope it comes back again in another form.