Given the example you gave, no quality management methodology can be applied.
Indeed, quality management is all about continuously improving the output quality (not only, but as an abstract overview, it is sufficient). This definition would itself need to be more properly defined regarding against which metric improvement would be measured, what is the output, what is quality…
These needed definitions and the continuous part are why you cannot have a fit: if your project delivers only once, there is no way you can measure a baseline output quality that you will try to improve upon.
To give some more details regarding PDCA, because putting PDCA and 6σ at the same level means your ideas are not so clear about both, and that PDCA is a good basis for understanding QM :)
If you look even only at the PDCA illustration:
…or read a bit about PDCA, you'll notice that “PDCA” is actually an iterative approach, and that we talk about PDCA cycles. A one-shot delivery has no way to get its output and processes Checked so that they can be Acted upon by updating the Plan (processes definition) for Doing the actual delivery.
PDCA is a basic framework that formalizes what many spontaneously do with a systematic approach.
6σ, on the other hand, is a strategy, i.e. a set of goals, methods, organizations and techniques, some of which are based on the PDCA cycle. And it would be overkill for any project of the kind you described, as it is designed for heavily industrialized and layered environments.