Prosthetic heart valve devices for percutaneous replacement of native heart valves and associated systems and method are disclosed herein. A prosthetic heart valve device configured in accordance with a particular embodiment of the present technology can include an expandable support having an outer surface and configured for placement between leaflets of the native valve. The device can also include a plurality of asymmetrically arranged arms coupled to the expandable support and configured to receive the leaflets of the native valve between the arms and the outer surface. In some embodiments, the arms can include tip portions for engaging a subannular surface of the native valve.