This paper introduces the concept of interval-valued T-spherical hesitant fuzzy set (IVTSHFS). Derived from the T-spherical fuzzy set, the IVTSHFS allows the membership, abstinence, and non-membership degrees of an element to be expressed as both interval and hesitant information. We present the basic concept, operational laws, and Hamming distance of IVTSHFSs and examine their fundamental properties. A novel score function governed by two adjustable coefficients is then developed, where λ serves as the preference coefficient and θ quantifies the degree of penalty for abstinence; an accompanying accuracy function is also constructed. Based on the operations of IVTSHFSs, two fundamental aggregation operators, namely the interval-valued T-spherical hesitant fuzzy weighted averaging (IVTSHF-WA) and weighted geometric (IVTSHF-WG) operators, are proposed. Furthermore, the power Heronian mean is extended to the IVTSHF environment, yielding the IVTSHF-WPHM and IVTSHF-WGPHM operators. To demonstrate the practicality of the proposed operators, a multi-attribute decision-making (MADM) method is developed within the IVTSHFS framework. A supply chain finance plan evaluation problem is then employed as a case study to validate the proposed method. Moreover, a systematic sensitivity analysis and comparative evaluation are conducted to rigorously assess the robustness and stability of the proposed method.