I do not have this problem, maybe I can shed some light onto this dreadful situation. So, I have full screen caller id on my iphone 5 ios7, I altered a few things though. I think what I did is the following. Ill have to explain from the start...
A while back I had a BlackBerry :O and it synced my contacts with facebook and the pics for caller id too (from their profile picture), when I transferred to my iphone 5 the same pics were there and I synced it with facebook again, not really sure if that changed anything. Anyway when I did the ios 7 update I had the same problem and so for my main/ most popular contacts I added a picture from my iphone photo library. Also some of my contacts e.g. Mum do not have facebook and so I also added this from my library. I already did some of this on ios6, but reapplied it again on ios7.
Also my main contacts are all in my favorites, maybe by putting it in the favorites list it makes it full screen caller id?
In short... try using a photo from your iphone photo library, and if you did this in ios6 do it again in ios7. You can also delete the picture afterwards and it still works. Then if that doesnt work put the contact into favorites.
Anyhow, this is what I did and it worked so hope it works for you too. 😀 Good luck.