Best check the iata travel center to see what countries you can enter and use that as a transfer point. I suspect with US residency there may be options. But the easiest is to bite the bullet and pay the going fare on the fastest, most direct route - and worry about the Orbitz ticket later.

If allowed to transit on a separate ticket in Dubai this would be a cost effective option. I do see award flights DOH-SFO but no way to get there direct.

I would also get a PCR test asap so you have that ready in case you do find an option.