EDIT to add: Speaking of 'Mockingbird' articles, you may be interested in Appendix A of http://dkeenan.com/Lambda/index.htm, whose author discusses another interpretation, attributed there to Barendregt, of Booleans and numerals. For someone who regards the Church encoding as 'intuitive', they were very surprising!
This was mostly just me trying to wrap my head around Church encodings and such, but I could surely do with a couple more combinators in there :).