This work presents a generalization of NchooseK, a constraint satisfaction system designed to target both quantum circuit devices and quantum annealing devices. Previously, NchooseK supported only hard constraints, which made it suitable for expressing problems in NP (e.g., 3-SAT) but not NP-hard problems (e.g., minimum vertex cover). In this paper we show how support for soft constraints can be added to the model and implementation, broadening the classes of problems that can be expressed elegantly in NchooseK without sacrificing portability across different quantum devices. Through a set of examples, we argue that this enhanced version of NchooseK enables problems to be expressed in a more concise, less error-prone manner than if these problems were encoded manually for quantum execution. We include an empirical evaluation of performance, scalability, and fidelity on both a large IBM Q system and a large D- Wave system.