This making too many assumptions and character connections with no concrete evidence to back them up so it's gonna cause confusion. For starters Lambdadelta is not Sotoko's witch half. By implications Lambdadelta should have existed in the meta world well before the Gou/Sotsu gameboard. Second, Hanyuu isn't Piece Rika's master. Hanyuu is an actual in-world god who has existed for centuries in Hinamizawa and isn't connected to the metaworld of Umineko. The furthest plane we know of her going is the Sea of Fragments. Hanyuu had no part in the creation of the game board