Because your running at low voltage you might be able to make a tap by sanding the outer insulation off the windings and solder on a wire, if you can find a point with the correct resistance you'll be able to do this, finding a point with less resistance will increase current.
I agree with les on shortening the core not making much diffrence, you'd just be shortening the magnetic path length, which will only have a small effect.
The core you used has laminations which are insulated from each other, chopping the end off has probably shorted them all togther, that probably isnt a problem either if your running it off dc.