My way round this would be by using a 'powercan' inverter (£15 from aldi bout a year ago) which has a 240v-150watt socket outlet & a 5v-5oomilliamp female usb outlet-the power lead is coiled and will stretch out to about 1 meter & theres a small switch on the side. Size approx 7in long by 3in diameter.
You could wire a spare fag lighter socket in parallel with snaplock connecters behind the factory fitted one so it hangs out behind the stereo (i have this setup for my snooper so the power lead is hidden and the plug end exits up against screen in the center,comes on with ignition & i dont loose the use of the fag lighter for satnav ect). Or alternately you could run a direct fused feed from battery via a relay switched from ignition live.
Dont know if the inverter would wedge behind stereo though but if so you could reach down to switch on/off so its not running when you dont need it as they do get quite warm more so when using the 240v outlet. Then run a usb male to female extension lead from inverter and mount in console/dash wherever you want.
Obviously dont plug too many/heavy drain items in normal fag lighter when inverter on or you'll blown the fuse which from memory is 10amp.
Hope this helps...rant over!