Fine-tuning large language models (LLMs) for sentiment polarity regression often suffers from severe data distribution imbalance. Financial texts typically concentrate in the neutral range, leaving extreme sentiments underrepresented, yet traditional techniques offer limited remedy since such extremes are inherently rare. We introduce an auxiliary classification task to provide complementary supervision, but this multi-task formulation faces two challenges: (1) sentiment group construction for the classification task, and (2) gradient conflicts between tasks that fixed weights cannot resolve. These challenges are coupled: improper group boundaries yield biased gradients, which amplify task conflicts. We propose the DRNash framework as a unified solution to jointly address both challenges and the underlying data distribution imbalance, including Distributionally Robust Optimization (DRO) and Nash Task Coordinator (NTC). DRO partitions the sentiment space into quantile-based groups and performs worst-case aggregation over group losses, automatically assigning higher weights to underperforming sentiment regions. NTC formulates task weighting as a Nash bargaining game, deriving closed-form weights that achieve scale-invariant balancing. Experiments demonstrate that DRNash achieves average improvements of 14.1% in MSE and 1.92% in accuracy (ACC) across multiple financial datasets, with cross-domain experiments confirming generalizability beyond financial texts.