Moving/animating particle systems on one axis

I'm trying to put together a simple starter 3D project in Unity free where a number(about 100) of particle systems in different places move towards the center of a plane at the same(slow) speed. All of the particle systems are rotated so they only have to move on their Z axis to get to that center.

My first idea was to animate each particle system by adding keyframes using Particle System Position.z, changing the Z position from 1 to 900 over 120 seconds. I thought I could just duplicate the particle system with the animation, move it to where I wanted in the scene and everything would work out hunky dory. I should have realized that when you duplicate the animation it duplicates the X,Y, and Z position animations too, so instead of my nicely spaced out particle systems all moving towards the center of the plane I got one big moving blob of particle systems instead.

If I could duplicate the particle system and ONLY the Particle System Position.z animation and not the Position.x and Position.y that seems like it would do the trick. Is this possible? It doesn't seem so from the animation interface (clicking on 'Remove Properties' next to the Position.x and Position.y seems to get rid of the whole Particle System Position curve all together).

It would be great if there was a straightforward way to do this from the GUI without getting into any scripting but it doesn't seem like that's the case(and probably better off learning sometime anyway!).

Does anyone have any pointers on how to approach this from a script?(Other non-script ideas welcome of course!).

I found a couple threads that might be relevant:

http://answers.unity3d.com/questions/188731/changing-particle-position.html

^^This one^^seems straightforward/digestible enough at first glance. It doesn't specify how to control the speed of it moving, would I use some sort of velocity variable?

http://answers.unity3d.com/questions/508192/how-to-move-particles-from-script-.html

^^This one^^seems to be specific to saying it only controls the position of the particles and not the whole particle system itself.

Thanks for any help!