In this study, we introduce an enhanced version of topological descriptors based on degree-distance invariants of connected graphs designed to effectively capture the structural characteristics of graphs with convex cuts, utilizing both vertex degrees and distances. We use this concept to analyze the Schultz and Gutman indices from reverse and neighbourhood degree perspectives. Motivated by the necessity for more effective descriptors in graph theory, our approach involves the development of algebraic expressions facilitating efficient computation, illustrated in some generalized benzenoid hydrocarbons. Moreover, the efficacy of the newly derived descriptors is evaluated through Linear and Quadratic Quantitative Structure-Property Relationship (QSPR) modelling on a dataset of carboxylic acids, and a set of structural isomers of saturated hydrocarbons revealing their effectiveness compared to existing descriptors.