Your suggestion is what should be done if done 100%correctly. I cheated.
I tried a shortcut (me?) that worked. I assumed that the blockage was probably at a ball valve and several pieces of stuff rather than one big piece. I turned off the water and bled the water pressure. Then I removed the galley sink wand from its hose, turned the regulator on the facet to HOT, and used some compressed air to blow the stuff backwards through the wand hose. Then, I turned on the water pump with the galley sink tap fully open to HOT, and out came all of the stuff.
I do not know about anyone else, but I have a air nozzle that I can attach to my dive tanks for cleaning things like carburetors and now galley sinks!
Currently Malta on the hard at MIYY