Hm… Moving Postgres instances across organizations is always a bit of trouble; I’m surprised to hear that the documentation’s officially recommended procedure wouldn’t actually be working at this point, though…
On the other hand, it does make sense that snapshots wouldn’t be available across organization boundaries, 
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I don’t have multiple organizations myself, to test, but others have reported success with a fly pg import + dual-organization Flycast combination. If no one chimes in with a better idea, that odd-looking but apparently effective technique might be worth a try.
Hope this helps a little!