In this paper, we construct and study solutions of Einstein's equations in a vacuum with a positive cosmological constant which can be considered as inhomogeneous generalizations of the Nariai cosmological model. Similar to this Nariai spacetime, our solutions are at the borderline between gravitational collapse and de Sitter-like exponential expansion. Our studies focus in particular on the intriguing oscillatory dynamics which we discover. Our investigations are carried out both analytically (using heuristic mode analysis arguments) and numerically (using the numerical infrastructure recently introduced by us).