  We develop a new simulation technique based on path-integral molecular
dynamics for calculating ground-state tunneling splitting patterns from ratios
of symmetrized partition functions. In particular, molecular systems are
rigorously projected onto their J = 0 rotational state by an "Eckart spring"
that connects two adjacent beads in a ring polymer. Using this procedure, the
tunneling splitting can be obtained from thermodynamic integration at just one
(sufficiently low) temperature. Converged results are formally identical to the
values that would have been obtained by solving the full rovibrational
Schr\"odinger equation on a given Born--Oppenheimer potential energy surface.
The new approach is showcased with simulations of hydronium and methanol, which
are in good agreement with wavefunction-based calculations and experimental
measurements. The method will be of particular use for the study of low-barrier
methyl rotations and other floppy modes, where instanton theory is not valid.
