Speech Emotion Conversion (SEC) aims to transform the emotion of a source utterance into a target emotion while preserving content and speaker identity. SEC on in-the-wild data is challenging due to the non-parallel nature of training data and complex real-world acoustics. Existing fixed-duration approaches either struggle to shift the emotion effectively (high quality, low conversion) or degrade speech naturalness (low quality, high conversion). We propose TargetSEC, an embedding-driven latent diffusion framework that generates emotion-focused style embeddings conditioned on speaker identity and continuous emotion. Unlike methods that diffuse over spectrograms, TargetSEC operates in a compact latent space. Experiments on the MSP-Podcast dataset show that TargetSEC outperforms current non-duration baselines in conversion accuracy while maintaining high speech quality, and achieves performance comparable to duration-prediction systems without explicit temporal modeling.