Have you done a plot of the frequency response of your sub? 'Slowness' may be attributed to room resonance, in which case a BFD would be a better bet to equalise the response. There is a slight difference between the Shiva and SV12, not enough to justify swapping in my opinion, you would be better off going for a 15" driver if you were thinking of changing.
One advantage you have is that the BSB500 is a very powerful amplifier, I would consider getting a Linkwitz Transform to boost the low frequency response of your sealed cabinet. A BFD can do this to a certain extent by the use of a house curve but it can't transform the Q of the sub. LT details here:
http://www.trueaudio.com/st_lkxfm.htm
You can get the bits from here:
http://sound.westhost.com/project71.htm
If you don't mind travelling you could bring your sub over to my house and we could try a Shiva in it (if it will fit) to see what you think. I also have a BFD and a Linkwitz Transform that you could have a listen to as well.