I think the easiest way to achieve axial movement of your chair (cockpit, etc) is to take advantage of the forcefeedback API. Take, for example, the Logitech Force 3D stick. It has two small motors that pull the stick in the X and Y direction based on output from the Aces High game. If you were to reroute that logic to larger motors that moved your chair rather than your stick then you would accomplish what you are describing. Obviously, you're dealing with some serious current with large enough motors to actually move a chair with a couple hundred pounds (in my case) of weight in it. That would involve some electronic design work but not as difficult as it may seem.
I've been thinking about this with respect to a squadmate that has a P51 cockpit he built but I haven't started experimenting yet. It is something I want to do at some point. I'm thinking a couple of automobile starters would work well for motors as they are 12V DC and have plenty of torque. Those motors are easy to find too.
Let us know if you make any progress on this. I'll do the same.
-mark