Recently, the makespan-minimization problem of compiling a general class of quantum algorithms into near-term quantum processors has been introduced to the AI community. The research demonstrated that temporal planning is a strong approach for a class of quantum circuit compilation (QCC) problems. In this paper, we explore the use of constraint programming (CP) as an alternative and complementary approach to temporal planning. We extend previous work by introducing two new problem variations that incorporate important characteristics identified by the quantum computing community. We apply temporal planning and CP to the baseline and extended QCC problems as both stand-alone and hybrid approaches. Our hybrid methods use solutions found by temporal planning to warm start CP, leveraging the ability of the former to find satisficing solutions to problems with a high degree of task optionality, an area that CP typically struggles with. The CP model, benefiting from inferred bounds on planning horizon length and task counts provided by the warm start, is then used to find higher quality solutions. Our empirical evaluation indicates that while stand-alone CP is only competitive for the smallest problems, CP in our hybridization with temporal planning out-performs stand-alone temporal planning in the majority of problem classes.