I was able to pull up LAX-IAD-BCN RT for $354 on all UA metal on ITA Matrix -- OTA is Priceline.

Search 9-day itineraries starting on Saturdays in September through end of October.

Not quite a mileage run, but good for a vacation maybe? You can also get mixed-metal itineraries (return via LH/LX) for shorter itineraries around $391 all-in.