I've seen an Xbox and a Gamecube combined before. I've also seen plans for similar ideas you have just mentioned. However, I don't think any of them have gone through, probably due to the amount of time required to do so, as well as modifying a PC case to hold the inards of all three (I would think a PC case would be the only thing large enough). However, if you'd like to do that, have a lot of time, and a mild budget (for buying the parts you will inevitably need to purchase), then by all means go ahead. You definately are not the first person to think of this, but you would be one of the few people to accomplish it.
Well... in theory, it's possible... (I believe the Xbox motherboard is single layer) I guess. However: have you seen that board?! I mean, after all, ouch! I don't think a soldering iron with a fine enough point exists in the world. So, unless you are a machine (I'm not trying to doubt your skills... but installing a mod chip and creating a motherboard are in a tad different league), I think you ought to stick to the original idea. Besides, two large cups are almost as long as the Xbox's length, so it's not like you need to remove three inches. You can make it shorter simply by moving the controller ports to the roof the Xbox, and it'll still be one of a kind.
- Greg