Alright im on the same boat as you guys, trying to get access to websites which are blocked by DET Portals whitelist. I just found out that they have just recently started using whitelists, becasue everything was coming up as "uncategorised". Also i think the idea of blocking "technical/business" is absurd and that the DET Portal should rot in hell, for doing that. I believe that the DET is using whitelists is to pre-ban anonymiser sites (commonly refered to as proxies).
My theory is that the use of a VPS will allow us to circumvent these blocks (not tested). A VPS (Virtual Private Server) is basically another computer. In order to access a VPS, you must first rent one from a VPS provider, then with the use of Remote Desktop Connection (Windows), you should be able to login to your VPS, and because your VPS is using another ISP, you should be able to circumvent these blocks.
A sure-fire method to circumvent these blocks is obviously with the use of a teachers account (tested I have done it myself), although the use of a teachers account will not be using the whitelist ban system, quite a number of sites are still blocked (annonymisers, warez, filehosts, etc.). To gain access to a teachers account, you must know the username and password (obviously). All students and staff on the DET Portal have access to password recovery questions (Hint: Use a teachers account from a past school, and also make sure they dont go online often). Further steps needed but will not be provided.