In practice, using an exact MCMC kernel (such as Generalized Hamiltonian Monte Carlo) for propagation would substantially increase the computational expense of a protocol by (a) introducing costly energy evaluations during accept-reject steps, (b) reducing the feasible integration timestep, and (c) dramatically increasing correlation times if the acceptance rate is even slightly less than 1. Including the shadow work contribution would also substantially reduce the acceptance rate of long protocols. In principle, though, one could simply use the total energy difference between the start and end states in the acceptance criteria; however, this would both lower the acceptance rate and lose the exact contributions of the protocol work and shadow work to the total work. Knowing their exact contributions is important to know how much the shadow Hamiltonian differs from the true Hamiltonian. In future work, we will examine the bias vs. efficiency trade-offs of our neglect of the shadow work, and the extent to which these can be mitigated by choice of Langevin integrator, or by using reduced-momentum-flipping variants of Hamiltonian Monte Carlo. While it has been argued more generically that the contribution of "shadow work" in nonequilibrium simulations can be neglected without introducing much bias, this is likely highly dependent on the specific choice of integrator used, so we recommend caution if other integrators are considered.