Your air compressor should have no trouble working the guillotine. What pressure is the air going to the guillotine set for? How much of a slice of timber are you cutting with each chop?
The other thing that I noticed is that the air cylinder returns the blades to full height each time. In the original foot operated mode a stop on the pedal limited this stroke. In your case the full stroke of the cylinder will be wasting a lot of air that your compressor needs to supply.
As for the blade lifting the timber on the return stroke, this is normally prevented by the fact that you hold the timber down with your hands when cutting. In your case I would look at fitting some clamps to hold the timber (like the sort that are fitted to SCMSs). This would give you a more accurate cut while keeping your hands away from the blades.
