I bought a GPS mount from radio shack that will either mount to the windshield with a suction cup or it has clips to hook to the vent which looks similar to the one you have.
I bought it originally for my HTC Evo 3d and I would clamp it long wise into the mount.
I have used the same mount for my Samsung GS3, my new Note 3 (Barely fits).
I have also used it with the Tab 3 7" I got for free from sprint but use the clamp on it top and bottom. I have also used it with my Nexus 7 (2013) short wise as well.
I just use a standard USB cable to connect to it which should work fine. You MAY be able to rig a Qi charger to the mount if you are industrious. Or just get a generic Qi car mount if one exists. I wouldn't do a specific tablet mount like that because in a year when you get a new tablet you will be buying a new one. I have had this mount now for like 3 years and used with 5 different devices.