There are two challenges, as I see it, that you need to control with your current setup. One is contrast, the other, speed.
Because the color temperature of household incandescent lamps is much warmer than enlarging lamps, your prints will be lower in contrast than if you had exposed them to unfiltered light under the enlarger. You can compensate with higher grade variable contrast filters, but you'll need to figure out a way to get the filters between the bulb and the paper with no light leaks.
Because enlarging papers are pretty fast, you'll need to cut down the light that reaches the paper. Avoid the temptation to use an inline dimmer to do this. Reducing the voltage to the lamp will not only reduce the output, but will lower the color temperature of the lamp even more. Again, lower color temperature = lower contrast with variable contrast papers.
[LIST][*]Switch from using enlarging speed variable contrast papers to graded contact speed papers. Both challenges addressed with a single solution. Contact papers these days are rare, but can be found.[*]Rig up a can with something similar to a grid spot and somewhere to place variable contrast filters. Then move it further away from the paper.