While prompt-based text-to-speech (TTS) models enable natural language-driven speaking style control, they often provide limited fine-grained control and apply a single global style across an utterance. This restricts practical use cases that require continuous style attribute interpolation across utterances and time-varying style transitions within a single utterance. In this paper, we propose novel techniques to achieve both capabilities in existing prompt-based TTS models. For inter-utterance style interpolation, we compute direction vectors between contrastive style prompts in the embedding space and perform simple interpolation, enabling smooth transitions between style characteristics. For intra-utterance style transition, we first identify a strong attention bias toward early tokens in autoregressive TTS decoders, causing the initial audio realization to dominate subsequent generation. To mitigate this effect, we introduce KV-cache swapping and sliding-window attention masking. Experiments demonstrate that our proposed inter-utterance interpolation achieves a 99-100% success rate in gender conversion, up to 36 Hz pitch variation, and up to 1.6 syllables-per-second speed change. Our intra-utterance transition maintains a speaker similarity of 0.81-0.91 and achieves perceptual smoothness scores of 3.48-4.48.