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Note to the reader: this exploit doesn't actually work due to RBF Rule #6.
tx_HS is considered to be a direct conflict, and its raw fee-rate does have to be beat directly. While ts_HS does spend an unconfirmed output, it appears that the fee-rate PaysMoreThanConflicts uses to calculate if ts_HS can be beaten is ts_HS's raw fee-rate. So looks like your understanding was incorrect on these two points.