A DONE3 is about $7700++ from the USA.
Generally, ROC-JFK-LHR (AA), then up to 4 flights within Europe, LHR-DEL(BA) or HEL-DEL(AY), DEL/BOM-HKG (CX), 3 more flights in Asia, HKG-JFK(CX). You have 5 more flights in N America. But you are only allowed 2 stopovers and the return to JFK is 1 of your 2 permitted stopovers. Outside of North America, stopovers don't matter except for tax purposes. Adding a rt to LAS or SAN is possible, but only 1.
You could start YYZ-LHR on BA and it may be a few $$ less. If you have AA evips, you can upgrade the AA long haul flights to FC, so the return from Asia could be via NRT or PVG.
A final factor is if your travels are after 1-Apr, you can use JAL, Royal Jordanian, and Malev Hungarian airlines.