flexible mounts for sanding table

[Frank S]

Now that I see what you were making. many of the ideas for movement control that were published would have worked equally well.
As for being violent there are 2 ways to tone that down one being mass the other being variable speed
many saber saws have a high and low speed others are variable I have one that has both
you could use a link bar between the saw and the plate with a pivot being closer to the plate than the saw something like 1.5 to 1 or what ever it took to reduce the total movement

Or you might try attaching a stiff extension spring to the plate then attach the other end to the saber saw this might dampen the stroke and the violence.
If that is not enough then attach a second spring to the plate where the first spring is connected and attach the other end to the base mount
I built a small gold sluice several years back using a similar spring set up