Every time I sync my iPad/iPhone it dumps all these old apps onto it.

(I have iTunes 11.0.4 and iOS 6.1.3 on my iPad for reference.)

I have a very specific set of apps I like to keep on my iPhone, and a specific set of different apps I want on my iPad, and it used to be that I could just uncheck "Sync Apps" in iTunes and I could manually organize these apps from either device. Now, though, my only option is to uncheck "Automatically install new apps" which does not even seem to be very helpful because every time I sync my phone or my iPad, iTunes dumps a seemingly random assortment (and perhaps even a random number) of old apps on. The only way I can see to prevent this is to painstakingly go through the list (of hundreds of apps!) and click "remove" next to every app I don't want. Is there any way to preserve the apps I have on my devices and prevent the app sync?

PLEASE HELP! For some reason I can only find year-old discussions that seem to pertain to this issue!