T[s[1,1]]

{{1,3,7,9,10,12,13,15,16,18,28,30,31,33,34,36,37,39,43,45,46,48,52,54},{2,4,6,8,11,14,17,19,21,22,24,25,27,29,32,35,38,40,42,44,47,49,51,53},{3,7,9,12,13,15,16,18,28,30,31,33,34,36,37,39,43,45,46,48,54},{4,6,8,11,14,17,19,21,22,24,25,27,29,32,35,38,40,42,44,47,49,51},{5},{6,8,14,17,19,21,22,24,25,27,29,32,35,38,40,42,44,47,49,51},{7,9,12,13,15,16,28,30,31,33,34,36,37,39,43,45,46,48},{8,14,19,21,22,24,25,27,29,32,35,38,40,42,44,47,49,51},{9,15,16,28,30,31,33,34,36,37,39,43,45,46,48},{10},{11},{12},{13},{14},{15},{16},{17},{18},{19,21,22,24,25,27,29,32,35,38,40,42,44,47,49,51},{20},{21,22,24,25,27,29,32,35,38,40,42,44,47,51},{22},{23},{24,25,27,29,32,35,38,40,42,44,47,51},{25},{26},{27,29,32,35,38,40,42,44,47,51},{28,30,31,33,34,36,37,39,43,45,46,48},{29,32,35,38,40,42,44,47},{30,31,33,34,36,37,39,45,48},{31},{32,35,38,42,44,47},{33,34,36,39,45,48},{34},{35,42},{36},{37},{38},{39},{40},{41},{42},{43},{44},{45},{46},{47},{48},{49},{50},{51},{52},{53},{54}}

MoveCount[i_,i_] := 0;
MoveCount[i_,j_] := T[s[i,j]][[3]];

Return[]

{126328,{{1,3,7,9,10,12,13,15,16,18,28,30,31,33,34,36,37,39,43,45,46,48,52,54},{2,8,19,21,25,27,38,40,42,44},{3,7,9,12,13,15,16,18,28,30,31,33,34,36,37,39,43,45,46,48,54},{4},{5},{6},{7,9,12,13,15,16,28,30,31,33,34,36,37,39,43,45,46,48},{8,19,21,25,27,38,40,42,44},{9,15,16,28,30,31,33,34,36,37,39,43,45,46,48},{10},{11},{12},{13},{14},{15},{16},{17},{18},{19,21,25,27,38,40,42,44},{20},{21,25,27,38,40,42,44},{22},{23},{24,29,32,35,47,51},{25},{26},{27,38,40,42,44},{28,30,31,33,34,36,37,39,43,45,46,48},{29,32,35,47},{30,31,33,34,36,37,39,45,48},{31},{32,35,47},{33,34,36,39,45,48},{34},{35},{36},{37},{38},{39},{40},{41},{42},{43},{44},{45},{46},{47},{48},{49},{50},{51},{52},{53},{54}},156105796449}

newgens = Generators[[{1,2,3,5,4,6}]]

gens =Rest[Generators];
g=0;
Print[Timing[
(++g; Feed[#]; Product[Length[Images[i]],{i,n}])& /@ newgens
]];
Print[tmc=TMC[]];
While[
Last[opt= Optimize[]] ≠ tmc,
tmc=Last[opt];
Print[opt]
]

Recycling