This paper presents SibylSat, a novel SAT-based method designed to efficiently solve totally-ordered HTN problems (TOHTN). In contrast to prevailing SAT-based HTN planners that employ a breadth-first search strategy, SibylSat adopts a greedy search approach, enabling it to identify promising decompositions for expansion. The selection process is facilitated by a heuristic derived from solving a relaxed problem, which is also expressed as a SAT problem. Our experimental evaluations demonstrate that SibylSat outperforms existing SAT-based TOHTN approaches in terms of both runtime and plan quality on most of the IPC benchmarks, while also solving a larger number of problems.