Previous work in phonologically and phonetically grounded language generation has mainly focused on domains such as puns and poetry. In this article, we present new work on the generation of tongue-twisters -a form of language that is required to be conditioned on a phoneme level to maximize sound overlap, whilst maintaining semantic consistency with an input topic and still being grammatically correct. We present TwisterLister, a pipeline for generating phonologically informed tongue-twisters from Large Language Models (LLMs) that we use to generate TwistList 2.0, the largest annotated dataset of tongue-twisters to date, consisting of 17K+ examples from a combination of human and LLM authors. Our generation pipeline involves the use of a phonologically constrained vocabulary alongside LLM prompting to generate novel, nonderivative tongue-twister examples. We additionally present the results of automatic and human evaluation of smaller models trained on our generated dataset to demonstrate the extent to which phonologically motivated language types can be generated without explicit injection of phonological knowledge. Additionally, we introduce a Phoneme-Aware Constrained Decoding module (PACD) that can be integrated into any causal language model and demonstrate that this method generates good quality tongue-twisters both with and without fine-tuning the underlying language model. We also design and implement a range of automatic metrics for the task of tongue-twister generation that is phonologically motivated and captures the unique essence of tongue-twisters based on Phonemic Edit Distance (PED).