I use preprocessor macros for what I guess I'll call "hyper-local extraction" in an attempt to be as DRY as possible. I don't know how modern C++ would handle this better. It looks a bit like this:

    #define a_ frob(-1,0,0); grob("a"); blah(...);
    #define b_ frob(1,0,0); grob("b"); blah(...);
    #define c_ frob(0,-1,0); grob("c"); blah(...);
    #define d_ frob(0,-1,1); grob("d"); blah(...);
    #define e_ frob(0,0,-1); grob("e"); blah(...);
    #define f_ frob(0,1,1); grob("f"); blah(...);
    
    if (normal_order) {
      a_ b_ c_ d_ e_ f_;
      c_ b_ a_ f_ e_ d_;
    } else if (special_order_1) {
      b_ c_ d_ e_ a_;
      d_ e_ c_ b_ a_ f_;
    } else if (...) {
      // ... and so on ...
    }
    
    #undef a_
    #undef b_
    #undef c_
    #undef d_
    #undef e_
    #undef f_