@Brian Black, a few thoughts.
15%: Seems very high. Standard is 8-10%. You're paying 1.5-to-2x average rates! No bueno.
Justify 15%: Have you asked your PM to justify the higher than industry rates? Perhaps it's all the maintenance, challenging rent collection, units are spread out across town, they include additional services you're unaware of (i.e. tenant placement guarantee, eviction protection).
Quality of Portfolio: What type of properties are in your portfolio: A, B, C, D grade? For newer dwellings or recently remodeled, it requires less work. As well, if your tenant pool has more stability and better credit, it's much easier to manage since rent collection is important. In a perfect world, your tenants pay with no reminders. Perhaps the 15% indicates a high risk portfolio that requires a lot of effort just to collect rent.
Some ideas/suggestions:
Co-Management: If you're willing to take on some of the management responsibilities, you could find a person hyperlocally to assist with some of the local tasks. Meanwhile, you could handle the tasks that do not require you to have a physical presence. By taking on some of that workload, you could reduce your management expenses.
On-Time Rent Bonus: If your property is lower income and higher risk, instead of the 15% then perhaps your PM would consider an on-time rent bonus. If the tenant pays on the due date, the PM gets .5-2% of rent as a bonus. If the tenants always pay on time then this probably isn't needed.