On reflection, I think we can safely ignore the bits and pieces in the tanks as causes of fuel starvation (scraper, paper, etc). Remember that there are 2 pumps in EACH tank. All four tank pump inlets would have to be blocked to cause the problems seen. Each pump is designed to provide enough pressure/flow to supply the onside engine with fuel for all flight regimes (and probably more). The lowest spec I've seen for a 777 wing tank pump is 12psi and 16tonnes/hr
I don't have the wiring schematics handy, but I believe the L/R wing tank pumps are powered by their onside Transfer Busses.
Rgds.
NSEU