Large-area, optically homogeneous monolayer semiconductors are a critical prerequisite for scalable room-temperature polaritonics and for realizing polariton lattices extending across many unit cells. Yet, the small size, optical inhomogeneity, and device-to-device variability of conventional exfoliated flakes have remained major obstacles. Here, we overcome these limitations using 1-dodecanol-encapsulated WS₂ monolayers that combine millimeter-scale coverage with remarkably uniform optical properties over lateral distances approaching 300 μ m. Integrated into a tunable open microcavity, these monolayers exhibit robust room-temperature exciton-photon strong coupling, evidenced by a pronounced anti-crossing and a Rabi splitting of ℏ Ω_R ≈ 31 meV. Leveraging the exceptional uniformity of this platform, we realize a two-dimensional polaritonic kagome lattice and directly resolve its characteristic band structure. Angle-resolved spectroscopy reveals Dirac dispersive bands together with a weakly dispersive flat-band-like branch within the s-band, in good agreement with a linear non-interacting model. Complementary momentum- and real-space imaging further identifies the associated bond-centered and site-centered mode profiles. These results establish large-area WS₂ monolayers in open microcavities as a scalable platform for engineering polariton band structures and exploring synthetic quantum materials under ambient conditions.