That is the problem with DMOZ. I don't know if it still works or not, but there used to be a way around the lengthy delays by creating an editor account with DMOZ in the category you are trying to get your site in. Once you as an individual are an editor you can approve your listing yourself for inclusion. I haven't played around with DMOZ in a long time so I don't know if this hack still works or not.
It used to be that Google gave juice to sites listed in DMOZ, but I am not really sure how much play that has any more. I would really focus on other avenues if that is why you are trying. I don't think DMOZ use is that significant that it will impact your rankings or site visits overall.