I don't think a multi-city or O/J is going to help you here. ARN is one of the cheapest markets for TATL business class travel, LHR/LON one of the most expensive. On top of that the LHR-SFO leg hits you with the maximum UK air passenger duty as a long-haul, premium-class flight (GBP150). With the three of you that's nearly $600 USD just in additional taxes. If you could find a competitive fare on British Airways SFO-LHR-ARN, you could probably do the stopover in London on the way back for "free" (extra taxes would still be calculated, though), but that might be significantly more expensive than SAS.
A nested ticket ARN > LON > ARN works fine, just allow some extra time on the way back to avoid misconnections. SAS has 5x daily LHR>ARN, so a delay of more than half a day is very unlikely.
You could also try ARN > LON > CPH to make your return trip a bit simpler as SFO-ARN / CPH-SFO may not cost you any more than SFO-ARN R/T.
Edited to add: also check Norwegian for ARN > LGW, they have 5x daily on this route and likely cheaper than SAS.