Research on dialogue constructiveness assessment focuses on (i) analysing conversational factors that influence individuals to take specific actions, win debates, change their perspectives or broaden their open-mindedness and (ii) predicting constructive outcomes following dialogues for such use cases. These objectives can be achieved by training either interpretable feature-based models (which often involve costly human annotations) or neural models such as pre-trained language models (which have empirically shown higher task accuracy but lack interpretability). We propose a novel LLM feature-based framework that combines the strengths of feature-based and neural approaches while mitigating their downsides, in assessing dialogue constructiveness. The framework first defines a set of dataset-independent and interpretable linguistic features, which can be extracted by both prompting an LLM and simple heuristics. Such features are then used to train LLM feature-based models. We apply this framework to three datasets of dialogue constructiveness and find that our LLM feature-based models significantly outperform standard feature-based models and neural models, and tend to learn more robust prediction rules instead of relying on superficial shortcuts (as seen with neural models). Further, we demonstrate that interpreting these LLM feature-based models can yield valuable insights into what makes a dialogue constructive.