I remember that on RB3 Xbox version, I do this:
1) Purchase/Download from some site the DLC you want to rip
2) Copy the DLC on a usb drive, if you have downloaded it on your xbox
3) Open the usb drive, then the CON package (the DLC package) with some software like Modio, or explore the usb with some other tool, and use C3 Con Tools to open the package.
4) Now navigate to a text file (I don't remember the name) where song settings were written.
5) Here you could find audio volume levels for each track.
6) Lower all of them, except the ones you want to rip.
7) Setup recording with an optic audio cable.
8) Play any instrument which is not the part you are ripping (I prefer the vocals, because it does not require to have all of the hardware instruments).
9) Repeat the process with every single track you are going to rip.
Tip: you could create more packages of the same song, by just changing the ID. You could even change the title. For example, you could have made five different version of the same song, but every one of them had lowered volume levels on specific tracks.
This ensures a better quality than phase inversion, and sometimes better isolation too, but you have always to sync tracks and adjust the global volume level.