Retinal fundus images frequently carry more than one disease, and public fundus datasets are heterogeneous and severely long-tailed. Clinical triage suggests a staged design, in which a screening gate, a disease-group router and group-specific classifiers operate in sequence, but it is unclear whether this hierarchy earns its complexity. We present a controlled comparison of three architectures on a unified 39-target label space built from RFMiD 1.0, RFMiD 2.0 and ODIR-5K (12,652 images): (i) a three-stage gated cascade of eight models, (ii) a flat model with 39 independent sigmoid outputs, and (iii) a label-correlation model that replaces the flat linear head with 39 learned label queries and a two-layer transformer decoder. All three share one Swin-V2-B backbone, one preprocessing pipeline and one training protocol, so differences are attributable to the architecture. Staging offers no consistent advantage: tracing every missed disease instance to the stage that lost it shows that the two coarse gates discard 34.2% of true instances while the fine-grained classifiers lose only 6.7%, and the gates' hard zeros depress the cascade's macro-AUC to 0.747. Label-correlation modeling gives the largest single gain, raising the detection rate from 0.621 to 0.682 (0.689 with test-time augmentation). Blending the flat and label-correlation models under four-view test-time augmentation is the best configuration on six of eight metrics (exact match 0.694, micro-F1 0.678, macro-F1 0.456, macro-AUC 0.972). On definition-matched class subsets it matches or exceeds four recent studies on macro- and micro-F1, most clearly on low-support pathologies. We also show that ensembling a gated cascade with continuous-output models is harmful, and that per-source negative sampling is needed to remove a dataset shortcut that otherwise yields a spurious AUC of 1.000.

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