That's when you start case modding
the HAF 912+ is a lovely case for your given requirements
Others to add to the list would be the NZXT BETA EVO
and LanCool K58 or K60 (these are a little over the budget) the only difference is that the k60 comes with two top mounted 140mm fans, you can fit 140mm fans in the top of the K58 but you need the Lian-Li screw kit to do it (or get creative) it only takes 140mm fans not 120mm fans
Main thing you'll struggle with though is positive pressure and a lower mounted psu, unless you set the top fans as intakes then you'll have more exhaust flow giving you a negative pressure case.
negative pressure cases do tend to cool better, mainly because the exhaust fans in a lower psu case are surrounding the hot cpu area so your dumping the hot air out of the case as quickly as possible by the shortest route.
The big down side to negative pressure is dust, air will get sucked in through every crack and crevice making it very hard to filter dust out.