Hi,
Wow this sounds like a real electromagnet alright.
Just to note, as Matt mentioned the winding of the coils could make a difference in the overall strength. It depends on how you intend to use the magnet, but most likely you'll use the entire face front which means you want the magnetic excitation in the center leg opposite to the two outer legs. In other words, if you hold the core up so you can view it as a big "E" then if the lower leg mag direction is left, then the upper leg mag direction should also be left, and the center mag direction to the right.
This means you could wind the lower arm with the wire starting at the right side and winding up and then back over the lower leg until you reach the main body of the "E", and the upper arm the same way, but the center arm would be wound starting at the main body of the "E" and winding the same way but progressing toward the end of the center leg (so from left to right instead of right to left).
The nice thing though is that the way you wind the windings is not as important as the magnetic flux direction itself. This makes winding the thing easier if you use three coils.
With this method, winding all three windings in exactly the same direction starting at the same point on each of the three legs (start at the main body or at the end of each leg). Looking at the "E" from the front face where the "I" is normally mounted this would look like all three coils were wound in the very same way in the same direction and starting and ending the same on each leg.
The trick then is to simply call the 'start' of the two outer legs on one end of the coil, and call the 'start' of the center leg winding the opposite end of the coil so that the current flows in the opposite direction in the center leg when you connect the power.
The other thing though is that when you wind onto the outer two legs you use up the window area for both sides. That means you can fit less turns on the center leg now. It is probably stronger with three coils even though we cant use as big a center coil, but i've never tried this and base this on the reluctance with consideration of the proximity to the work piece.
It sounds like you already have this working good enough so you probably dont have to change anything now anyway.