The additive manufacturing (AM) of continuous carbon-fiber-reinforced thermoset composites is becoming increasingly relevant in industrial settings as a means of producing high-performance structural components with a high degree of design flexibility. However, current AM techniques are often limited by the need for a thermal post-cure to achieve the desired mechanical properties. Frontal polymerization (FP) is a transformative technique for producing thermoset polymers and composites that relies on a self-sustaining polymerization front to cure the monomer fully. It has recently been demonstrated that FP is compatible with the AM of composite tows by combining the printer head with a pair of heated rollers that both consolidate and cure the extruded tow, in a process known as reactive FP direct ink writing. In this work, we describe a computational model developed to simulate the impact of process parameters on the stability of the FP reaction. We investigate the coupled effect of heating of the tow and extrusion speed on the front location. We also providing insights on a process optimization that reduces the need for the persistent heat source from the rollers by leveraging the natural propagation of the front. Lastly, we describe an extension to this process that enables AM of woven composite tubes, and study the impact of tube radius on curing.