Govehix,
Free advice from strangers is worth what you paid for it, but here's mine anyway...
Do yourself a favor - return those bass shakers and get yourself a good 8" subwoofer, a simple enclosure, and a decent amp. You will get what you are looking for - I promise. Those bass shakers are not really speakers - more like butt vibrators. They don't produce sound, they produce vibrations that you're supposed to feel in your seat. But if there's no real low-end sound to accompany them, they will "sound" pretty strange and awkward. They are marketed as a cheap alternative to a subwoofer setup, but you get what you pay for. There's only one way to get good sound - with amplifiers and speakers. There are no short-cuts, unfortunately.
Anyway, to answer your questions, if you were to wire them into the stock stereo, you would have to run a speaker-level (i.e., amplified) signal to them. The easiest way to do that is to connect them to the wires running to the rear speakers. However, if you do, you will be changing the rear channel loads on the stock amplifier (I won't go into the physics, the math, or the different ways they can be connected), and the amplifier will probably not handle that for long as it is almost certainly not designed to handle a load lower than 4 ohms. You need quality aftermarket audio products for that. SO the answer is, yes, you should get a separate amplifier for them if that's how you decide to proceed.
Furthermore, while there may be enough room under the driver's seat to mount the shakers, the TOD controller is under the passenger seat, so there may not be room to mount one on that side. And to make the situation worse, the seat has all manner of springs, levers, and rails running under it, and you will probably not find a solid flat surface to mount the shakers to. If they are not in contact with a solid surface, they will not transmit any vibrations, and you will have paid a bunch of money for nothing. Mounting them to the back of the seats will be a very inelegant solution, I think. They will cut into rear-seat footroom, and the rear seat passengers will likely end up kicking the wires off of them sooner or later.
When I got my VX, I was impressed with the clarity and dynamic range of the stock stereo, but the lack of low end was a problem for me. I bought a $130 Alpine 140W amp and an audiophile-quality Focal 8" subwoofer in a factory enclosure. That particular Focal sub and box run about $500 new, but I found mine on eBay for $200. The same amp and a JL Audio 8W3 subwoofer in a $100 enclosure would do the trick nicely. You can pull left-and-right speaker-level signals off the rear speaker wires WITHOUT affecting the stock stereo's amplifier load and run them into the speaker-level inputs on the amp. Contrary to what many car-stereo-buffs might believe, you will not be able to hear the difference in the sound quality by using the high-level input on the amp, especially in a subwoofer application.
With that setup, you will get what you are looking for, I promise you. You won't be blowing out the windows, but you won't be blowing out your eardrums, either, and the sound quality and bass "shake" will be there. The interior of the VX is pretty small in subwoofer terms, so you don't need much to get a good, strong, full sound. You will also be surpised by how much you can affect the feel and sound of the bass by changing the orientation of the speaker... face front for a dryer, tighter sound, face sideways or rearward for a louder, boomier sound.
It's obvious that you've put a lot of time and money into your VX, judging by your list of mods. Don't cheap out on the sound system - do it right with a sub and amp.