Well, I would try to mechanically damp the space between the front of the speaker and the cabinet. Maybe something like a rubber ring. Most speakers had some form of cushioned ring around the mounting surface, but on an old set they may be missing or became hardened.
These are the times I regret the old mouse pads went the dodo´s way after the modern optical mouse came out.
Those pads were great because when one needed some flexible, damping, isolating material, you could cut them into any shape. (In my country the hardware stores are not as well stocked as they should, and one has to improvise
. Maybe you can get something better off the shelf.)