Ok folks...I think I found a really good solution that does NOT involve a Power Inverter, but instead supplies 12V DIRECTLY to the XBOX via a DC-DC adapter, and bypasses the internal power supply entirely.
It requires a combination if two devices that someone on the MP3Car.com forums is using:
The fine print at the end of page 4 of the M1-ATX user manual says that the 5v and 12v rails combined cannot exceed 50 Watts. So If you need 2.5 amps for your 5v rail, that means you are using 13 watts of power there, and will have 37 watts left for your 12v rail, or a maximum of 3 amps. I would leave one amp alone (safety factor) and use the rest. Is 2 amp on the 12 volt rail going to be enough for you?
I am not an expert on this but from your numbers it seems to me your power consumption will be as follows:
12 v rail = .05 Amps or 1 watts
5 v rail = 2.5 Amps or 12.5 watts
3.3 v rail = 1 Amps or 3.3 watts
3 v rail = 0 mA or 0 watts
Total: 16.8 watts
12 v rail = 1.2 Amps or 14.4 watts
5 v rail = 15.7 Amps or 78.5 watts
3.3 v rail = 4.8 Amps or 15.84 watts
3 v rail = 20 mA or 1 watts
Obviously M1-ATX is not going to be powerfull enough to handle the x-box at full load. It looks like it will do the job at minimum load but I think your true consumption is going to be somewhere in the middle, around 65 watts or so. As long as you do not exceed 50 watts for 12v and 5v rails combined, it may work but it is going to be tricky!
Sounds like I should just keep the Wireless Adapter on it's own, and not try to use the M1-ATX to power it. Radio shack makes both a 4.5V and 6.0V cigarette ligher adapter, so which one am I better off with to provide 5.0V?