Vibration dampening

I suspect if your sub is vibrating you probably have it turned up way too much. Assuming you are talking audio and at volumes less than 100db then it should be filling in a thin band of low frequencies and well typically if you can hear it it is turned up way too high and is interfering with the overall audio spectrum.

When my subs were tuned in I could feel no vibration whatsoever with my hand on them.

+1 on the Aurelex SubDude II.

If you have watched many REL viideos you will know they strongly suggest to NOT use any isolation materials for their subs. I assume this should apply to any sub. The goal of setting up a sub or subs is to not know it is on until you turn it off. Think about that. My 212SX subs sit on a concrete floor with Blue Tac under them so on low organ recordings they do not slide. I do not have the issue you are describing. 

I use springs under mine ( a hint from millercarbon)  I also pull them out from the wall about a foot.  I feel the bass is tighter and less boomy.  A set of isolation springs was less than $30

I too use the springs under my sub and works well, about a foot out yes.