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Any chance the pits were egg incubator boxes designed to keep the eggs warm and covered in swan skin and feathers like the mother swan might do. Was there a black-market for swans? Might they have been raised for a profit and not a prophet? The unhatched ones could be the usual duds you get when incubating eggs. The smooth stones could be to store heat and keep the lonely eggs company. It seems more likely to be a mundane hatchery operation than facilities used to commit a reviled crime punishable by death. But then people might not continue to fund the further excavation of a ordinary poultry farm, but witchcraft! that piques the curiosity!

Leda and the Swan
W.B. Yeats

A sudden blow: the great wings beating still
Above the staggering girl, her thighs caressed
By the dark webs, her nape caught in his bill,
He holds her helpless breast upon his breast.

How can those terrified vague fingers push
The feathered glory from her loosening thighs?
And how can body, laid in that white rush,
But feel the strange heart beating where it lies?

A shudder in the loins engenders there
The broken wall, the burning roof and tower
And Agamemnon dead.
Being so caught up,
So mastered by the brute blood of the air,
Did she put on his knowledge with his power
Before the indifferent beak could let her drop?

Note: Zeus in the guise of a swan ravaging the maiden is an ancient tale commemorated in poems, paintings and rituals.