I think your problem is that your unbalanced connection is far too long. 15' is the recommended maximum length for an unbalanced connection. With very high quality cables you can under optimal circumstances get away with up to 25'.
You say you have feedback, but that is impossible with your arrangement. I suspect you mean noise.
The modern home is now a very noisy electrical environment because of the huge rise in switching power supplies, for instance LEDs and multifarious switching power supplies.
I think you have severe signal degradation and noise swamping. A signal booster will not help you as it adds more noise than signal.
I think you have two choices, convert to a balanced signal at the receiver and convert to unbalanced at the distribution amp.
Better buy a
high grade optical cable like this one.
You will need an audio digital converter at your receiver and a digital to audio converter at your distribution amp.
This latter solution is the best as this will give the best data transfer, and best of all optical cables are immune from interference such as RF.
In the modern home your connection is not correct and inadequate.