Multimodal alignment is critical for bridging the semantic gap in information retrieval. However, traditional pairwise strategies introduce a geometric blind spot: while they align anchor modalities (e.g., text) with others, they lack constraints to enforce mutual consistency between peripheral modalities (e.g., video and audio). The TRIANGLE framework addresses this by minimizing the area of modality triplets on a hypersphere to enforce holistic alignment. In this reproducibility study, we verify the robustness of this geometric objective for retrieval tasks. We confirm that TRIANGLE outperforms pairwise baselines in zero-shot settings, achieving Recall@1 gains of up to +8.7 points, though benefits are domain-dependent. However, we fail to reproduce the reported learning-from-scratch results. Analysis using a synthetic toy dataset attributes this to instability when jointly optimizing geometric alignment with Data-Text Matching (DTM) loss. Furthermore, we find that cosine regularization primarily stabilizes text-to-video retrieval, and fine-tuning with domain supervision amplifies geometric benefits but reduces cross-dataset generalization. Our findings support the efficacy of geometric alignment while highlighting critical optimization sensitivities. Code available at https://github.com/ARIJIT00171/RE-TRIANGLE.