A directory is some work to maintain, but it can be worth it and useful for your community.
The problem you pointed is the correct one, you don't want to be spammed.
Then, I am not sure about the script you're using, is it able to sort link into categories and to generate pagination ?
If it's only a page, then it's not meant to be used as a directory script, you should just accept 100% trusted links as you won't be able to put more than one hundred links in this page (more is not good for SEO).
All links on a single page is quite a limitation.
I see you managed to offer true Backlilnks, unlike the demo I tested.
Then, testing if the link is here when accepting the submission is not enough, this is something to check on a regular basis if you want to be sure.
The script I talked you about last time does not have any automated checking, but, you can only accept phpBB user to post links, which still have to get accepted, which can help out here to fight spam.