  We study the feasibility of nearly-degenerate two-photon rovibrational
spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular
ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking
advantage of quasi-coincidences in the rovibrational spectrum, the excitation
lasers are tuned close to an intermediate level to resonantly enhance
two-photon absorption. Realistic simulations of the REMPD signal are obtained
using a four-level model that takes into account saturation effects, ion
trajectories, laser frequency noise and redistribution of population by
blackbody radiation. We show that the use of counterpropagating laser beams
enables optical excitation in an effective Lamb-Dicke regime. Sub-Doppler lines
having widths in the 100 Hz range can be observed with good signal-to-noise
ratio for an optimal choice of laser detunings. Our results indicate the
feasibility of molecular spectroscopy at the $10^{-14}$ accuracy level for
improved tests of molecular QED, a new determination of the proton-to-electron
mass ratio, and studies of the time (in)dependence of the latter.
