Good ideas!
There should be relatively long times between steps since many contributers don't look everyday on this forum.
I propose a dodgson-hare synthesis method that I really like.
It' described in a good article : http://jamesgreenarmytage.com/dodgson.pdf with this abstract:
In 1876, Charles Dodgson (better known as Lewis Carroll) proposed a committee election procedure that chooses the Condorcet winner when one exists, and otherwise eliminates candidates outside the Smith set, then allows for re-votes until a Condorcet winner emerges. The present paper discusses Dodgson’s work in the context of strategic election behavior and suggests a “Dodgson-Hare” method: a variation on Dodgson’s procedure for use in public elections, which allows for candidate withdrawal and employs Hare’s plurality-loser-elimination method to resolve the most persistent cycles. Given plausible (but not unassailable) assumptions about how candidates decide to withdraw in the case of a cycle, Dodgson-Hare outperforms Hare, Condorcet-Hare, and 12 other voting rules in a series of spatial-model simulations which count how often each rule is vulnerable to coalitional manipulation. In the special case of a one-dimensional spatial model, all coalitional voting strategies that are possible under Condorcet-Hare can be undone in Dodgson-Hare, by the withdrawal of candidates who have incentive to withdraw.
Since we are not electing individuals but a method and a method cannot withdraw itself based on informed understanding - which is essential for the high strategy-resistance of this method - an modification seems necessary. For instance: everyone get's to nominate 1 method and can withdraw this method when there's a cycle. Perhaps a few times new additions can be allowed.