Dale, thank you for your helpful reply. I have a GFCI tester similar to what you show. Yesterday I also unhooked everything from the panel (including the power in!!) and still had no dice with the GFCI on the house. I strongly suspect that I either did something wrong when I rewired the inlet (likely) or that there is actually a short somewhere else (insulation rubbed through).
By re-wiring the inlet with fresh 10 gauge cable, I should be able to more easily test that the inlet is good. Then I can move on to systematically checking the panel wiring one circuit at a time as you described.