Are you aware that you can have a free stopover in your last North American airport on a LAX-LHR award?

You don't need to book a separate Southwest ticket. You can just book LAX-DFW and DFW-LHR and both flights can be priced as a single award. In addition, you can have a connection that is overnight too, so you can always fly late from LAX and catch the next day's flight.