@jack-waugh exactly, that's the kind of thing I'm considering. Now I'm kind of puzzled though about whether a head-to-head between two winners of clone-independent methods can fail independence of clones. I actually don't think it's possible that the composite system fails independence of clones. FYI my preference for a Condorcet method would be Tideman's Bottom 2 Runoff (B2R), which I'm now certain is equivalent to BNR. For example, we could even pit the Approval winner against the B2R winner head-to-head. That would be a form of Approval-seeded Llull with a final independent head-to-head.