If 'twere me (which it isn't) I'd put a coil in the flat bit, a high frequency oscillator in the edge, and a little ferrite coil, rectifier and overcharge logic in the little receiver units that plug in behind your phone. A little wasteful of energy, but we're not trying to make it boil a kettle.
The first use of this type of powering was in surgically installed pacemakers. It might well stay in health for surgically imbedded mobile phones/beepers/locators. Install a GPS in your baby, with remote interrogation, with a one of these under the blanket in his cot; you might never have to wonder where you left the pram again.
More worrying; why did people who had bought it frequently buy Tony Blair's memoirs? Are they rechargeable?