Every new clinical imaging device creates a domain shift where dense gland masks are expensive yet cheap clinical signals -- eyelid outlines, Pult grades, morphometric ratios -- are routinely recorded. We present TopoPult-SSL, a two-stage framework for cross-device meibomian gland segmentation. Stage 1 adapts a source-trained model without target gland masks in the training loss, using four weak-prior anchors driven by target eyelid masks and clinical metadata only. Stage 2, when target gland masks are available, distils complementary Stage-1 teachers into a single compact student via supervised self-distillation. We develop and validate the technique on the public MGD-1k to CAMG research benchmark (1,000 to 100 images, different device), where the distilled model achieves Dice 0.716+/-0.006 (best 0.726), surpassing UA-MT (0.710) and the ensemble teacher (0.720) -- with a single pass. The gland-mask-free Stage-1 variant reaches Precision 0.694 vs. 0.30-0.34 for SAM/MedSAM (p<0.001), enabling deployment without dense gland contouring. Code and reproducibility scripts are released.

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