Yet they were powerful enough to defeat Daedric Princes.
No they didn't. Dagoth Ur awoke in 2E882, meaning he had been active for about 441 years as of TES III. The Tribunal's recent failure to contain him was not due to colonization by outsiders, but more likely due to the Sixth House establishing a route underneath the Ghostfence through Kogoruhn, which they reoccupied in 4E400. In addition, the Ghostfence does nothing to stem the Curse-of-Dreams, nor does the presence of outsider races exasperate it (since it only affects Dunmer).
3E 417: Almalexia and Sotha Sil lose the artifacts Keening and Sunder to Dagoth Odros and Vemyn. Vivec rescues Almalexia and Sotha Sil, but failing to recover Keening and Sunder, the Tribunal retreat from Red Mountain in disorder. Surviving Buoyant Armiger companions know the Tribunal was forced to retreat, but do not know how serious a reversal the Tribunal has suffered. The Three Tribunes return to their respective capitals and continue to perform their ritual functions. The Tribunes continue to grow weaker without access to the Heart, and because of resources required to support the Ghostfence. The inner circle of the Temple priesthood has begun to suspect the Tribunes have suffered seriously from wounds and demoralization in the wake of reverses at Red Mountain, but do not recognize the scale of the problem.
http://en.uesp.net/wiki/Lore:Dagoth_Ur%27s_Plans