I do almost exactly that on a regular basis, only with TF700 and HOX+. Install and configure WebDAV server on your TF700T,
Just need to set up the right IP address on your wifi network. Then use ES File Explorer (or similar) on your phone to access all of the files on your tablet. You will be able to move, copy and even stream from your tablet (Including any files on an external hard drive connected to the tablet) directly to your phone. You just need to set up an FTP connection to your tablets WebDAV server you have started using the IP address etc.
You ideally would be on the same wifi network, but you can in fact set it up for wifi hotspot as well if no router is available. All the settings are remembered so you just need to start and stop the WebDAV server as you need and ensure that the wifi on your phone/tablet doesn't go to sleep. I wouldn't advise keeping the webdav server running all the time as this will possibly be a battery drain.
I can get anywhere up to around 5MB/sec transfer speed and it's pretty stable and reliable. You don't need root or anything to use the above method either. I'm pretty sure I have streamed full HD from hard disk, via tablet to my phone no problems. (with phone MHL HDMI in to my TV... just because I can!) but would normally just use tablet HDMI of course. I find it very useful to sync photos and important files.
To go one stage further you can use webdav file manager to set up auto sync, sync on schedule etc as well.
I use that to sync my picture folders.
Hope that helps as it took me a long time to find the right combination of programmes to make it work properly! I wish I could just plug my phone into the usb port and transfer that way as the speed is much better for large files over a gig or so.