I ended up booking OSL-LHR-JFK/BOS-PHX-LAS-DFW-BOS-LAX-MEL-SIN-DOH-DXB-DOH-LHR-OSL for about $7.4k. Taxes were a little more than I was hoping, but I suspect I could reduce it a bit by flying OSL-HEL-JFK or flying direct from DOH-OSL instead of flying through LHR.