I wouldn't cut some off my case to fit a GFX card in, but that's just me. I just don't feel comfortable doing that. If you want to, then don't let me hold you back; I just wouldn't do it. The way I see it, if you want to upgrade your graphics (btw, HUGE difference between 6600 and 6800GT), then it looks like you've got a couple options:
1) Get a different card
: Sell your X1800XT (not that it's a bad card at all; see explanation). You might be able to gain quite a bit of money, probably at the very least $200, possibly over $250 or 300, and that would be a great jumpstart for a DX10 card. Just keep in mind, you need Vista to run the card in DX10 mode; however, you can still run the card on Windows XP, it'll just be like DX9, but a really really fast one. One problem with waiting though: chances are that they will also take up two slots. Not a definite, but just a possibility.
2) Get a different motherboard, possibly needing a new case to go along with it. If you get either a Crossfire (recommended since you've got ATI) or an SLI board, those will have an extra PCI-E slot further down so you can fit the card in. Just make sure it will fit in your case first.
3) And of course what you said, cut some off the back of your case.
The motherboard option will probably be cheaper, but will require more work and you won't get DX10 with the X1800XT. But you do get to keep your card, which is a very nice one. Hope this helps.