We selectively excite and study two new types of phonon-polariton guided modes that are found in hexagonal boron nitride thin flakes on a gold substrate. Such modes show substantially improved confinement and a group velocity that is hundreds of times slower than the speed of light, thereby providing a new way to create slow light in the mid-infrared range with a simple structure that does not require nano-patterning. One mode is the fundamental mode in the first Restrahlen band of hexagonal boron nitride thin crystals on a gold substrate; the other mode is equivalent to the second mode of the second Restrahlen band of hexagonal boron nitride flakes that are suspended in vacuum. The new modes also couple efficiently with incident light at the hexagonal boron nitride edges, as we demonstrate experimentally using photo-induced force microscopy and scanning near-field optical microscopy. The high confinement of these modes allows for Purcell factors that are on the order of tens of thousands directly above boron nitride and a wide band, with new perspectives for enhanced light-matter interaction. Our findings demonstrate a new approach to engineering the dispersion of polaritons in 2D materials to improve confinement and light-matter interaction, thereby paving the way for new applications in mid-infrared nano-optics.