I don't see it working out. The back slot openings on a case are slightly recessed and the card slides into place to fit into the pcie slot. There's no place for the second tab on the bottom of a dual height gpu to fit and nowhere for it to slide into with only half the openings available meaning it will put pressure on the card trying to shove it forward just a bit to the front of the case. That strain would be placed on the pcie slot on the motherboard and you'd have to jam it in to make it fit. Something tells me you'd end up with a damage pcie slot trying to make it fit. Best to get a compatible case if looking to crossfire if it won't fit your current card placements.
Or like basroil suggested, try your hand at a power tool and...