Twisted, coiled polymer actuators (TCPAs) are a promising type of fiber-based actuators with high energy density, low material costs, and good recyclability; however, current manufacturing methods limit the length and stability of TCPAs, hampering their potential for large-scale textile applications. To overcome this limitation, we propose a textile manufacturing method based on the false-twisting principle, allowing for continuous and rapid production of highly twisted monofilaments. Additionally, this process enables the plying of two or more twisted monofilaments together, as well as the integration of wires for heating and sensing purposes. The resulting twist-stable plies can then be mandrel-coiled and annealed to create a new class of TCPAs with three superimposed levels of helicity, in contrast to the usual two levels. In this study, we investigate the impact of the additional helix level and various factors, including twist density, annealing temperature, cooling speed, and chirality, on the contractility of these TCPAs. Furthermore, due to the twist-stability of the plied yarns, they can be processed on standard textile machines, enabling the manufacture of TCPAs with multiple active yarns that can form contracting artificial muscles using a circular braiding machine. Our key findings reveal that the twisted monofilament coils can contract up to 60%, and higher twist density leads to improved performance for monofilament TCPAs. Notably, this phenomenon is not observed in plied-yarn TCPAs, where varying levels of twist on the monofilament and yarn helix level result in enhanced contractile performance. Overall, this work presents a novel textile manufacturing method for producing twist-stable TCPAs with good contractile performance, providing insights into the design and fabrication of advanced fiber-based actuators for potential applications in large-scale textiles, robotics, and biomedical devices.