Multi-Agent Pathfinding (MAPF) is a fundamental problem in AI, robotics, autonomous logistics and digital entertainment. This study focuses on the MDD-SAT encoding strategy for the MAPF problem. Traditionally, Conflict-Driven Clause Learning (CDCL) SAT solvers have dominated SAT MAPF solutions. This work explores an alternative approach: leveraging Stochastic Local Search (SLS) SAT solvers, specifically variants of ProbSAT, to solve MAPF with edge conflict prevention using MDD-SAT encoding. Our experiments on standardized benchmarks show that CDCL solvers excel in complex problems. In contrast, ProbSAT variants outperform CDCL in simpler scenarios, when given informed initial assignments derived from Multi-Valued Decision Diagrams (MDDs). Additionally, we propose a restart procedure to enhance SLS solver robustness. This study provides critical insights into the strengths and weaknesses of CDCL and SLS solvers and highlights opportunities for hybrid approaches, paving the way for further optimization in MAPF applications.