I found C space using Expert Flyer and successfully upgraded LAX-LHR and LHR-JFK-CLT-DEN. Return trip is the day before Thanksgiving, so seats are out there. DEN-LAX is waitlisted, but it's an E175 with no service to speak of so I'm not bothered.
When you are searching using EF be sure to check each segment individually; connecting flights will show C7 consistently when the actual C count is low or nonexistent.