There is a complex inclination structure present in the trans-Neptunian object (TNO) orbital distribution in the main classical-belt region (between orbital semimajor axes of 39 and 48au). The long-term gravitational effects of the giant planets make TNO orbits precess, but nonresonant objects maintain a nearly constant "free" inclination (Ifree) with respect to a local forced precession pole. Because of the likely cosmogonic importance of the distribution of this quantity, we tabulate free inclinations for all main-belt TNOs, each individually computed using barycentric orbital elements with respect to each object's local forcing pole. We show that the simplest method, based on the Laplace-Lagrange secular theory, is unable to give correct forcing poles for objects near the {nu}18 secular resonance, resulting in poorly conserved Ifree values in much of the main belt. We thus instead implemented an averaged Hamiltonian to obtain the expected nodal precession for each TNO, yielding significantly more accurate free inclinations for nonresonant objects. For the vast majority (96%) of classical-belt TNOs, these Ifree values are conserved to <1{deg} over 4 Gyr numerical simulations, demonstrating the advantage of using this well-conserved quantity in studies of the TNO population and its primordial inclination profile; our computed distributions only reinforce the idea of a very coplanar surviving "cold" primordial population, overlain by a large I-width implanted "hot" population.