Cyclic Weak Levenquine
>&lt;>, Score: 41

'd3*}&gt;a!o-!&lt;&lt;8:5@lI55&gt;@z:5ll55&gt;&gt;q:&gt;|q::|,


and the disjoint program

"r00gr40g44++bb+0p64++?b6+0.22&#23;#e&#23;W4s )Z&#29;


Try it online!

A copy of my answer to the Mutually Exclusive Quine question. A mutually exclusive quine is made of two programs, A and B sharing no common characters, where A outputs B and B outputs A. This means it is a 2-cycle Levenquine and also qualifies for this question. This can act as a baseline for other more inventive answers (though I'm not very confidant this won't go the way of the original Levenquine question).

A more detailed explanation can be found here.