permissionpreferences
Specifically I would like to edit com.apple.applicationaccess.new.plist. (Which is in /Library/Managed Preferences/[username]/), but when I restart the computer my edited preferences are replaced with the old version.
How do I go about editing them for good? I only have command line access via SSH.
Open preferences and check the box marked "Load preferences from a customer folder or URL""
You can browse to your Dropbox folder and the click "Save Settings to Folder"
An erroneous extended attribute has been applied to this directory somehow, but it can only be removed using the xattr Terminal command. You should take a look at a brief explanation here. A more detailed question and answer can be found at this StackOverflow page.
Best Answer
Turns out that the master copy of com.apple.applicationaccess is kept in
/private/var/db/dslocal/nodes/Default/[user].plist. Editing that solved the problem for me. Thanks to Lyken for helping me find this on this question.