Monitoring the vertical progress of reinforced-concrete buildings supports construction management, urban analytics, and seismic exposure classification, yet camera-based floor counting faces two obstacles: public datasets depict almost exclusively completed structures, and the number of structurally finished floors is visually ambiguous while a building is still being erected. We reformulate building-height estimation as discrete floor-count classification from a single street-level facade image and assemble a 29,049-image multi-source corpus centered on the reinforced-concrete urban stock of Kazakhstan, including a 12-month, fixed-viewpoint sequence of 2255 frames that isolates invariance to construction stage, illumination, weather, and season. We formalize a reproducible annotation protocol for three recurring structural ambiguities—incomplete upper floors, rooftop superstructures, and open ground-level pilotis—and propose DINOv2-MSTS, a dual-branch architecture that aggregates multi-scale patch-token statistics from a frozen self-supervised backbone, trained with an Ordinal-Aware Annotation-Uncertainty (OAU) loss for which its Gaussian spread is learned rather than fixed. On the 5359-image Korter + Mendeley 21-category benchmark, the model attains 80% top-1 accuracy, 94% within $\pm 1$ floor accuracy, and 0.28-floor mean absolute error on this saturated 21-category task (a lower bound for buildings of 21 or more floors) using only 1.84 M trainable parameters, 165× fewer than a fully fine-tuned Vision Transformer, which it outperforms by eight accuracy points. On the separate 2255-frame IITU fixed-label robustness probe, it preserves the correct six-floor prediction in 91% of frames (0.09-floor MAE). The corpus, protocol, architecture, and loss together provide a reproducible benchmark for construction-stage building monitoring.