Is there a way of remotely changing multiple iPad's locks/homescreens to the same custom image all at once over the air (not via USB)? I currently compile profiles with Apple Configurator, but changing wallpaper is apparently not possible with MDM. Isn't there a app or something that can do this?
This is currently not possible OTA. You must connect the device over USB to change the wallpapers.
You can change the wallpaper of a supervised iOS device remotely via MDM. There is a "Managed Setting" command available for this.
Here is an excerpt from the Apple MDM documentation.
A wallpaper change is a one-time setting that can be changed by the user at will. This command is supported in supervised mode only.
iOS 9 will also introduce a restriction to forbid changing the wallpaper on supervised devices.
It's just a question if your vendor has implemented it or not.