From my experience getting out that drive bay is almost impossible without wrecking the case, it's probably bolted or soldered. I don't think you will be able to cut it without industrial tools.
You could try to see if you can take off the graphics card plastic cover BUT it will probably void your warranty and there is a chance it's not possible or could cause damage to the card.
The best thing to do would be to get a new case - you could take everything out in the meantime and run the computer with mobo sitting on the desk - very rough but works
In case you do something like that, just make sure not to put anything conductive under your motherboard, plastic spacers/supports would be the best.