Text-based speech editors expedite the process of editing speech recordings by permitting editing via intuitive cut, copy, and paste operations on a speech transcript. A major drawback of current systems, however, is that edited recordings often sound unnatural because of prosody mismatches around edited regions. In our work, we propose a new context-aware method for more natural sounding text-based editing of speech. To do so, we 1) use a series of neural networks to generate salient prosody features that are dependent on the prosody of speech surrounding the edit and amenable to fine-grained user control 2) use the generated features to control a standard pitch-shift and time-stretch method and 3) apply a denoising neural network to remove artifacts induced by the signal manipulation to yield a high-fidelity result. We evaluate our approach using a subjective listening test, provide a detailed comparative analysis, and conclude several interesting insights.