(A) After some looking around on the web last night I found that my statement "Correct me if I'm wrong but the cheaper see-saw roller type (Roland, etc.) vinyl cutters also use Theta axis control" was incorrect. I see that most if not all roller type (Roland, etc.) vinyl cutters use trailing blade.
(B) Here's another homemade vinyl cutter attachment link:
http://cuttingedgecnc.com/vinyl.htm
As far as I know, even if the blade can only be up or down it would still be referred to as the Z axis.
My ESAB router (3m x 2m working area) is the same as your vinyl cutter. It's either up or down (mine uses a pneumatic cylinder) even though I plan to convert in the near future to full Z axis control. Even though it can only be up or down, I've always refered to that movement being Z axis even though it's not microcontrolable as that is the direction of the movement. Maybe I'm wrong on this point as well? I don't know.
And lastly just to clarify my statement earlier in the thread, the Theta axis I was talking about is for the motorised rotational (360deg) control of a tool (in this case I was refering to a vinyl cutting blade)
Skippy