PCI-E cards are secured partially by the mechanical strength of the slot, but primarily by being screwed to the chassis at the end where you plug the cables in. This isn't a mistake I'm aware of anyone making.
My best guess is that you've bought dual slot graphics cards and are trying to put one in the lowest slot. I didn't know the 250 was dual slot, but if it isn't your post makes no sense. This requires a case with eight pci slots cut out the back. I believe the Antec 1200 has seven.
My akasa omega has eight slots. All you're looking for is a large box covered with flashing lights with eight slots in the back. You should be able to count these from a photo if need be. I'd look to Silverstone.
I feel it has to be said, tri sli with gts250 makes very, very little sense. I'm sure you have your reasons for going down this road, but perhaps a better solution is to just use two of them, or to replace one with a single slot version.