After you completely erase the volume, install OS X using OS X Recovery as you described. Do not use "Restore from Time Machine backup". After it completes, create a brand new, temporary account using a name that you can dispose of later.
Use the machine in this configuration and satisfy yourself that everything basically works properly after multiple shutdowns, reboots, and logins.
If you find no problems, use Migration Assistant to migrate your existing User account from the Time Machine backup. Log in to that account and satisfy yourself that everything works the way you expect, including verification that it still has Administrator privileges. Your previous work environment should be restored in this manner.
After that, you may delete the temporary account you created after installing OS X.