I appreciate your in-depth analysis and I enjoyed reading it. I never thought too much about this theme, so it's cool to stop and consider what its meaning might be. And I think you're right that we shouldn't consider it a theme for the medallion. You make a great point that there are too many missed opportunities to use the theme if that was really what it was for. I also think you're correct that this and the ark theme are two distinct themes, even though they may appear together (similar to the Rise of Skywalker trio/victory themes). I haven't seen the film in a while, so I'll have to give this some thought next time I see it.
I disagree that the theme is strictly about "sin" as you suggest, but I think you're on the right track. Williams does a fantastic job at writing themes that don't just signal when a specific character or other story element appears onscreen, but represent whatever that character or thing represents. Often, his themes even express some larger undercurrents and themes of the film itself. Notice each Star Wars film has heroic themes, romantic themes, evil themes, and they're usually associated with specific characters, but they also reflect larger requirements of the story.
Here's how Williams described Luke's theme in an interview:
Note the last line there. Luke's theme isn't just describing Luke's character, but the specific qualities he represents or possesses that are important to a heroic story like Star Wars.
The themes in Raiders of the Lost Ark function the same way. The Ark theme doesn't exist only to address the physical object, or signify when it's on screen. It fills the role, musically, of expressing an important driving force of the film - the awesome power of God that is not to be trifled with. And the theme has a dark quality to it that directly foreshadows what ultimately happens when it's opened.
So, with all that said, I think it's possible that the "medallion" theme is also meant to represent the ark, and some of the things the ark represents. But maybe it suggests slightly different ideas about the ark (and the film). "Sin" could be one of those things, although its meaning is probably broader than that. I would guess Williams wrote both themes loosely around the ark, and then chose to deploy one theme or the other as he intuited was appropriate for each scene. Compare it to the situation with the two themes for Kylo in The Force Awakens. What was on his mind when he wrote two themes for the same character? Well, we don't really know for sure. But we can agree the two themes express different qualities of the character, so they are not completely interchangeable. But it might also be a mistake to try and pigeonhole them by assigning strict meanings beyond the idea that they're themes for Kylo. Maybe we should describe these two ark-related themes by their mood, similar to how we talk about Kylo's themes, e.g. Kylo (tragic).