Salaam and Ramadan mubarak to you...
There is basically no chance for you to get the -200LR out of ORD...
If you want, you should just fly to YYZ, then you will get a 99% chance of flying on the 777-200LR...in fact, that is what I plan on doing, Inshallah if I decide to take PK..
My route would be....SJC-ORD-YYZ-KHI...