Exclusive neutral-pion electroproduction (ep → e^'p^'π⁰) was measured at Jefferson Lab with a 5.75-GeV electron beam and the CLAS detector. Differential cross sections d⁴σ/dtdQ²dx_Bdϕ_π and structure functions σ_T + εσ_L, σ_TT, and σ_LT as functions of t were obtained over a wide range of Q² and x_B. The data are compared with Regge and handbag theoretical calculations. Analyses in both frameworks find that a large dominance of transverse processes is necessary to explain the experimental results. For the Regge analysis it is found that the inclusion of vector meson rescattering processes is necessary to bring the magnitude of the calculated and measured structure functions into rough agreement. In the handbag framework, there are two independent calculations, both of which appear to roughly explain the magnitude of the structure functions in terms of transversity generalized parton distributions.