i had seen this video before, but taking your advice, i took a good look at it again, and i found my problem. my caliper does not have a quick release on it, but it does have a hollow screw (?) that the cable passes through and a nut. i found that by increasing the distance between the nut and the top of this hollow screw (by backing the screw out and securing it in place with the nut), i could take up even more slack and have the lever engage the cable more effectively. after some adjustments, my brake pads now engage the rim with a lot more force.

thank you for all of your advice. one more question though: are there different levers that can pull more cable than others? thank you all again.