Icelandair is £2500 in J...
Often, you'll find that so long as the last international segment starts after the first sunday, you'll be OK. So, if you book LHR-SEA-LHR on your dates then on to AMS or somewhere on the Sunday afternoon (maybe from Gatwick

), you'll hit the Saturday night stay restriction.

and the AA codeshares seem a bit better at this.
A twist on the IT fares above is also to book a flight & car with BA.com - they'll throw in a natty Hyundai Accent for 6 days with the flight for £1013. (You don't even need to go collect the car....)