Magnetic Field Interfering with Radio Waves
As an additional option for your design, consider adding blocking elements to separate the wireless transmission of power from signal transmission.  These could be Faraday cage style meshing dumped to ground or (possibly) some nickel based sheet metal stock.  If it's easier to just move the receiver for data transmission, do that.  If not, or if for some other reason you'd rather not move that receiver then maybe you can corral your signals using metal.  

Here's a (wikipedia) example of EM shielding inside an old cell phone:  https://en.wikipedia.org/wiki/Electromagnetic_shielding#/media/File:Electromagnetic_shielding_inside_mobile_phone.jpg