You did not specify your KSU, but a M7310 does not contain any user programming. The user programming profiles results in the KSU and software associates that profile to the DN a phone is connected to. Hence, none of your spare phones have "pre-programmed" features. They may have button caps and labels on them, but the actual function of a key or button is all dependent on the central KSU profile.
A simple set swap would be to keep things connected as they "were" and go into programming and be sure set relocation is turned off. Then pull the failing set out and put it aside and take your spare M7310 and connect it to the jack where the DN 701 is punched, let the phone boot up, and it will have the same "buttons" and extension number as the old phone did. (You may end up transferring labels from the old phone's button caps to the replacement set).
If you replace the M7310 with another model of phone, you may not get the seamless transfer of user features.