This trip can theoretically be done in FC for $4.068. $3,110 in C. And FWIW, these are published fares mind you!!! But you DO need to be really, really cleaver... and have some status w UA and CO. UA to the west coast. PR. Then CO. Interestingly, the PR flight has a technical s/o in GUM (SFO-GUM is ns), but psrs CANNOT layover there - so one does need to backtrack MNL-GUM.

I noticed, too, that there were lots and lots of other options in C that were large chunks less than the amounts that have already been mentioned here.

In short, find yourself somebody that knows what they are doing, and save yourself $2,900 of that 6K budget!