  Panhandle matroids are a specific lattice-path matroid corresponding to
panhandle-shaped Ferrers diagrams. Their matroid polytopes are the subpolytopes
carved from a hypersimplex to form matroid polytopes of paving matroids. It has
been an active area of research to determine which families of matroid
polytopes are Ehrhart positive. We prove Ehrhart positivity for panhandle
matroid polytopes, thus confirming a conjecture of Hanely, Martin, McGinnis,
Miyata, Nasr, Vindas-Mel\'endez, and Yin (2023). Another standing conjecture
posed by Ferroni (2022) asserts that the coefficients of the Ehrhart polynomial
of a connected matroid are bounded above by those of the corresponding uniform
matroid. We prove Ferroni's conjecture for paving matroids -- a class
conjectured to asymptotically contain all matroids. Our proofs rely solely on
combinatorial techniques which involve determining intricate interpretations of
certain set partitions.
