Not sure that saturation is the reason for the problem that you are seeing. However, to avoid saturation by adding an air gap: if your windings are on the central leg of the E, and all the I parts are stacked together making a block, it should be quite easy to separate them. Remove from the frame the two screws that hold the I parts , lift off all the I laminations, file the holes in the frame to allow for a gap, add a few sheets of mylar across the end-face of the E, reassemble.