What happens when buoyant force causes movement to exceed sound speed?
High buoyancy and low speed of sound have conflicting requirements. A low molecular weight increases buoyancy but it also increases the speed of sound at a given temperature. Similarly, for a gas a at least, high temperature increases buoyancy but it also increases the speed of sound. How about a liquid or solid at very low temperature? The mere act of condensation brings the molecules so much closer together that the speed of sound increases. To lower it back down again you must increase the molecular weight, which reduces buoyancy. The only variable left to play with is pressure: for a gas, low pressures increase buoyancy up to a point but has no effect on temperature. On the other hand, if the molecular weights of the object and medium differ considerably, then pressure has ittle effect on buoyancy either. All, in all, even if it were possible to find a combination of materials and states which fulfilled the basic criteria, it would only be by a modest amount. But see below.
The killer then is drag, caused primarily by frontal area, skin area and poor streamlining. A long, thin object has lowest frontal area, a sphere the lowest skin area but worse streamlining. So you are caught with a teardrop-shaped compromise. Drag rises with the fourth power of speed, so you do not have to go very fast before it equals the buoyancy. This speed is known as the terminal velocity. Your only hope for near-sonic speeds for any medium would be a frictionless fluid, i.e. superfluid helium below 2.1768 deg K (says Wikipedia), and probably confined in a capillary tube, making your experiment microscopic (I'm not sure at what scale the transition to conventional drag occurs, but it is small).
You now have to find a material which is less dense at this temperature than liquid helium. There are no gases down there and no other liquids, even hydrogen is solid. Aha! Solid hydrogen is less dense (0.0763 g/ml) than superfluid helium (ca. 0.13 g/ml).
So there you have it. A microscopic grain of solid hydrogen in an arbitrarily tall capillary tube filled with superfluid helium. I look forward to your posting on ArXiv ;)