In the planning-as-SAT paradigm there have been numerous recent developments towards improving the speed and scalability of planning at the cost of finding a step-optimal parallel plan. These developments have been towards: (1) Query strategies that efficiently yield approximately optimal plans, and (2) Having a SAT procedure compute plans from relaxed encodings of the corresponding decision problems in such a way that conflicts in a plan arising from the relaxation are resolved cheaply during a post-processing phase. In this paper we examine a third direction of tightening constraints in order to achieve a more compact, efficient, and scalable SAT-based encoding of the planning problem. For the first time, we use lifting (i.e., splitting) and factoring to encode the corresponding n-step decision problems with a parallel action semantics. To ensure compactness we exploit reachability and neededness analysis of the plangraph. Our encoding also captures state-dependent mutex constraints computed during that analysis. Because we adopt a lifted action representation, our encoding cannot generally support full action parallelism. Thus, our approach could be termed approximate, planning for a number of steps between that required in the optimal parallel case and the optimal linear case. We perform a detailed experimental analysis of our approach with 3 state-of-the-art SAT-based planners using benchmarks from recent international planning competitions. We find that our approach dominates optimal SAT-based planners, and is more efficient than the relaxed planners for domains where the plan existence problem is hard.