Several works published over the last two decades have shown for a stylized set-up with homogeneous users that metering-based priority (MBP) schemes may generate Pareto improving departure time adjustments similar to those induced by congestion pricing, but without any financial transaction. We investigate whether MBP (i) still generates significant savings and (ii) remains Pareto-improving, with various sources of heterogeneity (in schedule flexibility, desired arrival time, and capacity usage). We consider two types of schemes: one where the priority status is allocated randomly (R-MBP) and another (HOV-MBP), which only prioritizes users with small capacity usage (e.g., carpoolers). We find that the relative total cost savings of R-MBP decrease with heterogeneity in flexibility, but may increase with heterogeneity in desired arrival time. It fails however to be Pareto-improving, as nonprioritized users are almost systematically worse-off. HOV-MBP circumvents this issue by generating an ordering effect and a modal shift, which both contribute to a better distribution of benefits among users. Under favorable circumstances, they may even restore a Pareto improvement. Overall, MBP appears as a realistic way to alleviate congestion, scoring well both in terms of efficiency and social acceptability.