Wikipedia says no efforts to measure the mass of 33 Polyhymnia have been made since 2012. The scientist who estimated its mass at that time regarded the result as nonphysical and in error.

Couldn't this mass be much more accurately estimated by sending a small probe of known mass by the asteroid at a known distance and velocity, and measuring the trajectory perturbation?

I think this could be done with a 5kg radar reflector. No guidance, no comms, no onboard electronics at all. Terrestrial radar measurements of position and velocity are extremely accurate. The launch wouldn't have to achieve super accurate trajectory, just good enough to see gravitational perturbation.

Not much of a launcher needed for this. It might even work as a ride-along payload. Could be a relatively low-cost way of resolving this weird density result.