I work a lot with sat solvers, but with using in a proper language. Either cbmc for C (not Klee, not Z3 as these require extensive translations to obscure languages), or picat for a proper functional language with support for normal non-functional coding styles.
The sudoku sample is a few lines there, and it used to win many CSP contests. http://www.hakank.org/picat/sudoku_pi.pi
cbmc is esp. nice to autocreate proper test cases.