Should anyone ever come across this question of mine in search for answers to a similar problem, here is what I did:

Use Rhinoceros (4.0), it has a command which does exactly what I needed. Export as .obj from maya, import in rhino. I then put in a plane and use the array command on it, specify the instances' vertical distance from each other to the amount I needed and then used the intersect command (I don't remember if I used meshes or converted to surfaces at some point, try it out). That gave me the slices of my model that intersected with each plane as a curve.

There is a Plug-In for Rhino which I could not try out due to some error, which is called RhinoNest, which I suppose does this trick in an automated manner. It seems this whole issue is not really in Maya's area of operations, as it is more of a CAD-thing.

If you want to try this/need to do this (the way I did it) and need help, you can send me a PM and I will respond ASAP.
I will also try to do this in Inventor as soon as I have the time and give an update.