Cannot restore from backup, not enough space on iphone

I am using an 8G iPhone 4, and iTunes 12.2.2.25 on a 64 bit Windows 7 PC.

In April 2013, I moved to another country, and my sister received my iPhone while I was away. I backed up my iPhone to my PC just before I left. She cleared the history and started it over as something new. She deleted many apps and added some service updates that worked for her, as it became her primary phone.

Now, I'm back, and my sister is no longer using this phone. I want to restore my iPhone to the settings I had when I was using it, but every time I try to perform a backup, I get an "Not enough space on iPhone to restore" error. There is over 1.5 gigabytes of free space on the iPhone. I have tried rebooting my PC, rebooting the iPhone, upgrading iTunes, disabling my firewall, resetting (and restoring) the Lockdown folder, everything.

I do not want to simply resync the apps or the contacts I had. I want my phone to be just as it was two years ago. There are apps that are no longer available in the store that I want to use, as well as videos that do not appear to have been backed up.

What can I do?