If you want to "upgrade" the Alexa rank, install the Alexa toolbar and visit your own site several times over the course of the day. Get your co-workers to do the same thing. You will see your rank improve quickly.
If you don't want to go through that trouble, it's not that hard to program a script to launch a browser and visit your site on your behalf. Just set it up on a spare computer with the toolbar installed and let it run all day.
The point is, the "Alexa rank" isn't going to be improved by getting a DMOZ listing. The Alexa rank measures the number of visits to your site by people who have the Alexa toolbar installed.
Because it only measures visits by people who have the toolbar installed, Alexa doesn't give a good representation of actual website traffic. If you want to know how your site traffic is improving, use a web log analysis program or install Google Analytics (it's free).
Alexa is very easy to manipulate and it doesn't measure anything particularly useful. It might be better to explain to your boss why Alexa rankings aren't worth tracking and instead try to focus on measuring (and improving) things that really matter -- like sales and revenue.