I see. I can't help you with the PSU because that question is just way too specific. Almost everyone just gets regular PSUs, I have no knowledge about such special cases.
However, if you are having that much trouble I would strongly suggest getting a new case after all. Changing the PSU already requires a lot of work with all the cables needing to be replaced. Unscrewing the motherboard and putting it in a new case is probably less work than the whole re-cabling.You'll probably want to upgrade to a much better rig at some point in your life. Whether it is when games get more demanding, when there is a specific game you really love or when you start earning more money, at some point you'll wanna upgrade and cases are not nearly affected as badly as other parts by the progress of technology. The only technology in cases that has changed recently is USB3, which can also be provided by motherboards or PCI cards.