In this paper, we introduce a novel methodology for leveraging shape-based characteristics of magnetograms of active region (AR) patches and provide a novel capability for predicting solar flares covering the entirety of the solar disk (AR patches spanning from -90$^{\circ}$ to +90$^{\circ}$ of solar longitude). We create three deep learning models: (i) ResNet34, (ii) MobileNet, and (iii) MobileViT to predict $\geq$M-class flares and assess the efficacy of these models across various ranges of solar longitude. Given the inherent imbalance in our data, we employ augmentation techniques alongside undersampling during the model training phase, while maintaining imbalanced partitions in the testing data for realistic evaluation. We use a composite skill score (CSS) as our evaluation metric, computed as the geometric mean of the True Skill Score (TSS) and the Heidke Skill Score (HSS) to rank and compare models. The primary contributions of this work are as follows: (i) We introduce a novel capability in solar flare prediction that allows predicting flares for each ARs throughout the solar disk and evaluate and compare the performance, (ii) Our candidate model (MobileNet) achieves a CSS=0.51 (TSS=0.60 and HSS=0.44), CSS=0.51 (TSS=0.59 and HSS=0.44), and CSS=0.48 (TSS=0.56 and HSS=0.40) for AR patches within $\pm$30$^{\circ}$, $\pm$60$^{\circ}$, $\pm$90$^{\circ}$ of solar longitude respectively. Additionally, we demonstrate the ability to issue flare forecasts for ARs in near-limb regions (regions between $\pm$60$^{\circ}$ to $\pm$90 $^{\circ}$) with a CSS=0.39 (TSS=0.48 and HSS=0.32), expanding the scope of AR-based models for solar flare prediction. This advancement opens new avenues for more reliable prediction of solar flares, thereby contributing to improved forecasting capabilities.