A note on 10awg romex. Yes, the wire is extremely stiff and you may not be able to install it. You CANNOT fold this wire when pushing the outlet back into the box. It is just too stiff. When I did mine, I had to run the Romex straight through the wall from behind into the junction box and then "square bend" one wire at right angles so that there's enough space. A 12awg romex would definitely be much easier to handle.
If you have the room in your wall you can use a deeper outlet box to make the job easier.