The present technology is a prosthetic heart valve device, and related systems and methods, for treating a native valve of a human heart having a native annulus and native leaflets. One embodiment comprises a valve support having an inflow region and an outflow region, and a prosthetic valve assembly within the valve support. The device further includes an anchoring member having a base attached to the outflow region of the valve support, a plurality of arms projecting laterally outward from the base and inclined in an upstream direction in a deployed state, and a fixation structure extending upstream from the arms. The fixation structure has a plurality of struts that define an annular engagement surface configured to press outwardly against the native annulus and a plurality of fixation elements projecting from the struts. The downstream-most portion of the fixation structure extends from the arms at a smooth bend, and fixation elements at the downstream-most portion of the fixation structure extend in an upstream direction.