I always connect at Dulles or JFK for my Europe flights, and I'll have two different flight numbers. Once in a while I'll connect at ORD (for instance, to get to Dusseldorf) when there isn't an east coast connection.

SFO-LHR nonstop 5,368 miles
SFO-IAD-LHR 6,096 miles
SFO-JFK-LHR 6,052 miles
SFO-ORD-LHR 5,799 miles

Pretty much works the same from SEA:

SEA-IAD-LHR 5,983 miles
SEA-LHR 4,801 miles

Throw an east coast connection in there for Europe flights and you'll get more miles. Just make sure you ticket as two segments each way, versus a "through" flight if the flight numbers remain the same. You'll pay a few dollars extra in taxes, but the miles will make up for it.