Packing the pump is a moot point now, and generally not necessary. They don't pack them at the factory where they make these engines, and you don't remove and repack the pump every time you suck air because you were upside down or such.

Packing is helpfull for priming the pump when cranking it over dry on the starter motor. That's a slow spin, and the pump sometimes doesn't do a good job of pulling the oil up initially then. As soon as it starts though, it pulls it up.

You've got oil, so the pump is getting it up. Ie, it's primed. Now what the pump is actually doing, and the rest of the oil circuitry, that's another question.

I'm going off memory here, but as I recall, the back of the oil pump has a seal where it bolts up to the block. If that seal is missing/damaged, you'll be losing oil via that seal and not getting it up to the galley.