Despite the many benefits of large language models (LLMs), they can also cause harm, e.g., through automatic generation of misinformation, including conspiracy theories. Moreover, LLMs can also ''disguise'' conspiracy theories by altering characteristic textual features, e.g., by transforming their typically strong negative emotions into a more positive tone. Although several studies have proposed automated conspiracy theory detection methods, they are usually trained using human-authored text, whose features can vary from LLM-generated text. Furthermore, several conspiracy detection models, including the previously proposed ConspEmoLLM, rely heavily on the typical emotional features of human-authored conspiracy content. As such, intentionally disguised content may evade detection. To combat such issues, we firstly developed an augmented version of the ConDID conspiracy detection dataset, ConDID-v2, which supplements human-authored conspiracy tweets with versions rewritten by an LLM to reduce the negativity of their original sentiment. The quality of the rewritten tweets was verified by combining human and LLM-based assessment. We subsequently used ConDID-v2 to train ConspEmoLLM-v2, an enhanced version of ConspEmoLLM. Experimental results demonstrate that ConspEmoLLM-v2 retains or exceeds the performance of ConspEmoLLM on the original human-authored content in ConDID, and considerably outperforms both ConspEmoLLM and several other baselines when applied to sentiment-transformed tweets in ConDID-v2. The project will be available at https://github.com/lzw108/ConspEmoLLM.