http://net2ftp.com/ - You can either connect through their web interface or install it on your own hosting account, it's far from ideal but if you have no way of changing your ftp port or tunnelling through your school's network it may be one of your only options.
Net2Ftp has a PHP based (and therefore kinda open-source, free) that i've set up a few times. I dont turn on the logging, but it can log 90% of what users do (put file, list dir, etc). It only has 1 admin password, but htpasswd/htaccess can fix that on Apache. You could also easily patch it for multiple users.
cronjob to clean up the spare stuff (it assumes it has /temp available)