Hi Adam, I've done similar experimentation using both tungsten and led bulbs but have found that, even with multigrade filters, I was struggling to get the sort of contrast I wanted.
I had a set up like what joe suggested, bulb in a can with a 10mm hole at the bottom, covered with a piece of tracing paper.
Unfortunately, I don't think this system is suited to multigrade papers. Like joe said, azo papers had a much longer exposure time and were, if I'm not mistaken, graded rather than multigrade.
My solution was to pick up a really cheap small enlarger from the bay and an enlarger bulb (cost £40 = $60?) and have had much better success contact printing 5x4 negs.