The entropy-driven monolayer assembly of hexagonal prisms and cylinders was studied under hard slit confinement. At the conditions investigated, the particles have two distinct and dynamically disconnected rotational states: unflipped and flipped, depending on whether their circular/hexagonal face is parallel or perpendicular to the wall plane. Importantly, these two rotational states cast distinct projection areas over the wall plane that favor either hexagonal or tetragonal packing. Monte Carlo simulations revealed a re-entrant melting transition where an intervening disordered Flipped-Unflipped (FUN) phase is sandwiched between a fourfold tetratic phase at high concentrations and a sixfold triangular solid at intermediate concentrations. The FUN phase contains a mixture of flipped and unflipped particles and is translationally and orientationally disordered. Complementary experiments were conducted with photolithographically fabricated cylindrical microparticles confined in a wedge cell. Both simulations and experiments show the formation of phases with comparable fraction of flipped particles and structure, i.e., the FUN phase, triangular solid, and tetratic phase, indicating that both approaches sample analogous basins of particle-orientation phase-space. The phase behavior of hexagonal prisms in a soft-repulsive wall model was also investigated to exemplify how tunable particle–wall interactions can provide an experimentally viable strategy to dynamically bridge the flipped and unflipped states. © 2021 Elsevier Inc.