[Kaiba]

However, one thing I remember is in ep4
The sin I am now demanding that you remember is not between Ushiromiya Battler and Beatrice.
"Ushiromiya Battler has a sin."
"Because of your sin, people die."

Your theory doesn't really support this and I think it's more vital in this mystery. By your theory the motive for killings are actually not connected to Battler at all, it's about George and his ambitions. I don't think it's going to be as simple as George killing everyone in order to live a rich life with his love.

The first truth doesn't work against it because the sin is not between Battler and Beatrice, it is between Battler and Shannon. I guess I would apply my Shannon = Beatrice theorem loosely. Shannon isn't Beatrice directly, she acts as the Beatrice of the island throughout the murders and so forth.
Battler's sin is that he didn't keep his promise to Shannon, and if he had kept his promise, Shannon probably would not have been persuaded into the whole murder plan of George, and thus the plan would not have gotten off the ground as George would not have had not nearly as much motive to kill everyone and without Shannon would lack much of the means in the first place to commit those murders.

Using your theory it would be pretty weird that the "masterminds" Shannon and/or George die so often, and early too.

Not really. I'll basically sum up what I think happened in the episodes:
Episode 1: Shannon fakes her death, the two are working with Nanjo, who persuades the others that Shannon is dead. Shannon proceeds to run amok afterwards and kills virtually everyone else (Kanon's death is explained by a trap being laid there as Shannon uses the place as an escape route, but I have also not completely ruled out Shkannon.)
Episode 2: The two work with Genji and Nanjo at first, and things go according to plan for a bit. However, someone figures out those two and kills those two, but the rest of the family kill each other out of fear and paranoia.
Episode 3: For whatever reason, Shannon starts backing out of the plan, and George in a panic ends up killing her and all the servants as a way to cover it up and follow the epitaph. The pair thus this round don't really do anything, but someone else (depending on the situation, but I suspect Kyrie in a lot of the scenarios) starts killing people, and the family breaks down as once again they kill each other out of fear and paranoia.
Episode 4: Not really sure, that arc was so damn weird. I'll have to think harder about that one later.
Episode 5: The two are planning to work with Genji, but Battler solving the riddle throws everything in disarray. George and Genji want to keep going so they can keep the gold all to themselves, but Shannon, due to her love for Battler, decides "fuck it" and kills George and Genji, and then kills the other three because they're in the same room as George to make sure she gets away with it. I really don't know anything about the rest of the arc, so I can't really explain Krauss's and Hideyoshi's deaths as I don't know anything about them.

Different reasoning but similar conclusion compared to my theory. There is just a noticeable error: the riddle wasn't disclosed until 1984, so in 1980 didn't exist, and Battler couldn't have made such a promise.

Oh dear, I didn't realize that. Perhaps then the promise was just a childhood marriage promise and Shannon didn't want to reveal the gold's location as she wanted Battler to be the first to see it. I guess that works them.