You got your solution right there mate. Go talk to your supervisor about it. If he/she has any semblance of a human being, they would know that a PhD is tight on funding and if they knew the repercussions of not assigning you work, they will try and help for sure.
Very inspiring motivations there! As one working in public sector myself, I can safely say it is your passion for helping others that will get you far. Anyone joining the public sector for any other reasons will find the journey very tough and unrewarding.
For me, I think its a good thing to do the test at home. It's an environment that is much more familiar, and using my fast laptop beats the old 10 year old desktops at the test centers by miles.
That being said, perhaps you can try doing the test in the wee hours of the morning while the rest of your family are asleep for the best results?
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