A versatile, stochastic version of the pom-pom model is proposed and employed to reexamine the nonlinear stress relaxation of a nearly monodisperse H-shaped polyisoprene melt. Since the current simulation model requires less assumptions and approximations to solve the stretch relaxation of entangled H-polymer chains, the pom-pom model proposals can be tested independently and rigorously. Detailed comparisons are made among the current stochastic simulation, the predictions of the original model, and a set of stress relaxation data. At short times right after the imposition of a large strain sufficient to induce complete arm withdraw, the proposals concerning an initial partial cross-bar retraction are well supported by showing close agreement between the simulation and the nonlinear relaxation data. On intermediate time scales when a renormalized cross-bar retraction was predicted to set in, the essential properties of stress relaxation are also largely consistent with the early theories that considered dragstrain coupling along with a dumbbell-like cross-bar retraction. The most obvious discrepancy is found for the nonlinear relaxation at long times, where the data begin to exhibit systematic deviations from the predictions assuming complete cross-bar retraction near the renormalized Rouse time. The last finding is discussed in conjunction with recent experimental observations regarding the possibility of a partial stretch relaxation upon the Rouse time.