I've noticed that puzzles that can be solved with CP-SAT's presolver so that the SAT search does not even need to be invoked basically adhere to this (no backtracking, known rules), e.g.:

    #Variables: 121 (91 primary variables)
      - 121 Booleans in [0,1]
    #kLinear1: 200 (#enforced: 200)
    #kLinear2: 1
    #kLinear3: 2
    #kLinearN: 30 (#terms: 355)

    Presolve summary:
      - 1 affine relations were detected.
      - rule 'affine: new relation' was applied 1 time.
      - rule 'at_most_one: empty or all false' was applied 148 times.
      - rule 'at_most_one: removed literals' was applied 148 times.
      - rule 'at_most_one: satisfied' was applied 36 times.
      - rule 'deductions: 200 stored' was applied 1 time.
      - rule 'exactly_one: removed literals' was applied 2 times.
      - rule 'exactly_one: satisfied' was applied 31 times.
      - rule 'linear: empty' was applied 1 time.
      - rule 'linear: fixed or dup variables' was applied 12 times.
      - rule 'linear: positive equal one' was applied 31 times.
      - rule 'linear: reduced variable domains' was applied 1 time.
      - rule 'linear: remapped using affine relations' was applied 4 times.
      - rule 'presolve: 120 unused variables removed.' was applied 1 time.
      - rule 'presolve: iteration' was applied 2 times.

    Presolved satisfaction model '': (model_fingerprint: 0xa5b85c5e198ed849)
    #Variables: 0 (0 primary variables)

    The solution hint is complete and is feasible.

    #1       0.00s main
      a    a    a    a    a    a    a    a    a    a   *A* 
      a    a    a    b    b    b    b   *B*   a    a    a  
      a    a   *C*   b    d    d    d    b    b    a    a  
      a    c    c    d    d   *E*   d    d    b    b    a  
      a    c    d   *D*   d    e    d    d    d    b    a  
      a    f    d    d    d    e    e    e    d   *G*   a  
      a   *F*   d    d    d    d    d    d    d    g    a  
      a    f    f    d    d    d    d    d   *H*   g    a  
     *I*   i    f    f    d    d    d    h    h    a    a  
      i    i    i    f   *J*   j    j    j    a    a    a  
      i    i    i    i    i    k   *K*   j    a    a    a

Together with validating that there is only 1 solution you would probably be able to make the search for good boards a more guided than random creation.