I just pulled apart my Solidtek ASK-6600U, which has the same ringing issue. I think the problem stems from two issues--the metal plate used to hold the switches is relatively thin (you can bend it in your fingers), and the swtiches are soldered through the metal plate, onto the PCB, and it doesn't appear that anything else is holding the metal plate in place.
If there was a non-conductive, expanding foam you could spray in between the PCB and plate, it should help reduce the resonance, but I'm not sure how / if that would affect the individual swtiches.
As an experiment, I sandwiched some non-condutive padding in around the edges of the PCB and metal plate, and sandwiched another piece between the entire key / plate / PCB assembly and the plastic case, and it helped a bit, but not completely.
If I held the key / plate / PCB assebly in my hand to absord the vibration, and pressed some keys, the ringing was gone. So, at least in the case of the Solidtek, it's not the switches themselves resonating, but the plate / PCB assembly.