Sync app problem

Hi everyone,

I had the iOS7 beta on my iPhone 5, but I wanted to reset it to the latest 6 since I'm not that big of a fan (yet).

Problem is that I needed to set up my iphone as a completely new iphone. When eventually putting up an older back-up, it didn't transfer all my apps. It did transfer a few, but a lot of them didn't transfer (new and older apps).

The strangest thing is that I can see them all in my iTunes library..
My iPhone is connected via Apple ID and I already tried the "transfer purchased app" option thing.

Any ideas?

Downloading them all again is not an option. When I go to the iTunes store, they are marked as already downloaded.