Couldn't you still do the ITA search across wide ranges of geography and get a sense for where the best fares are? I remember years ago I had a string of cities (maybe 10 or 15) where if you entered them into ITA with +300 miles, it was effectively searching all of Europe in a single query. There were strings for every geography imaginable - I remember using the Western USA one as well.

That would reveal that the oddball Montana destination happens to have unusually good fares right now, and since we generally know the relationships between a BE fare and a non-BE fare on a given route, it'd be easy to go to the airline website and make sure you buy the non-BE fare.

Been a couple years since I've searched this way, but ITA still looks like it always did so it should work, right?