Mirroring iPhone 4 (iOS 7) to Mac without AirPlay Mirroring
I don't have any experience with jailbreak, but I think one possible solution would be to see if you can run a VNC server on the iPhone.  VNC is a screen sharing protocol: the server runs on the machine whose screen you want to view and control, the client runs on the machine that you want to sit in front of.

I did a Google search for "iPhone VNC server" and came up with this link which describes how to set up Veency (jailbreak required) to do this.