Can't download videos (new or purchased) anymore - since iOS 7

iPad 3 (64 gig, ATT). We have iPads 1,2 and 4 (all 64 gig, ATT) as well, but this issue is only on iPad 3.

In addition to the plethora of issues others iPad 3 owners have experienced, the one that's causing me the greatest consternation is the fact that I have rarely been able to successfully download videos from the iTunes store (either new or purchased) since upgrading to iOS 7. Have tried multiple fixes:

• I have to reset my ipad probably a dozen times a day now
• I've done two complete "reset to factory settings" through iTunes 11.1
• I've reset all content and settings via Settings
• I've even taken my ipad to different places to see if it's somehow related to my wifi connection (which, before iOS 7 worked just fine on my iPad)
• Manually stop the new feature that allows up to three videos to download at once (which helps sometimes, but not often)
• Tracked to see if it's related to file size - anything over 1 gig is guaranteed to not download.
• Also tracked to see if there's a different success rate between new and purchased content. New has a better shot at successfully downloading. Purchased is more than 90% fail.

So, two things typically happen when I try to download a video:

1. the file downloads to the point where the status says "Processing file." Then it dumps the download and immediately says "preparing to download." It will continue doing that for a few minutes, then show an error message that says "unable to download: done or retry." Retry takes you back through the same cycle and same results. Done just cancels it...but if you retry from the same file later, same results. I've even deleted the files and come back later to try to download. Same result. But it rarely actually installs the video.
2. Or it starts downloading and then locks the ipad and requires a reset (no matter how long i leave it...i've even left it overnight just to see). When it restarts and I click to try downloading again, same thing.

So, at best, I'm having about a 10% success rate downloading videos to my ipad. I'm stuck downloading to my computer then transferring. I know, first world problems (cry a tear for me). But it worked perfectly before iOS 7...and I'm hoping there's a way to get back to the same level of basic functionality.

Any suggestions?