That could be a very tight budget, if you go with ground, precision ball screws of that length. One thing I am lacking is a good mental image of what you are trying to do. My experience with shears is that the blade is set to a specific gap tolerance so that it avoids interference with the other blade and provides a proper shearing action. A fairly wide range of material thicknesses can be cut without changing the blade settings.
Your description makes it sound as if the blade(s) are being set for cutting different sizes of material. In my experience, sizes are set with various stops, not the position of the blade. Is the blade being adjusted because there is a wide variety of materials and thicknesses being sheared every day?
Directly to your question and for that budget, I think I would focus on making the manual adjustment easier rather than trying to make the adjustment automatic. For example, modern digital readouts and linear scales for machine tools can be obtained for about that much money and would facilitate adjustment.
John
Edit: Just saw Ken's post (#8). We are talking about the same thing.