There is an option in the main menu "Start New" - ( Start the Run from the beginning)
You can also select the difficulty but this option does not keep the cars from the previous game.
Using another Persona/Username cannot provides you an access to these cars, you will be consider as a new user and also technically this does not seem to be possible unless you want to merge two Origin accounts (some limitations may apply) or something similar.
The only option would be the Checkpoint Resets but this is not exactly what you are looking for from what I understand and I guess you already know how this option works.
Checkpoint Resets are triggered when you wreck your car, and once activated, they send you
back to the last passed checkpoint. Resets can also be triggered manually, which can give you
the opportunity to improve the time of the last section you raced. Keep in mind that you are given
a certain number of Resets per race, and using up your last one results in failing the event. Your
chosen difficulty determines the number of Resets you are given.
If you reach the end of a stage with Checkpoint Resets remaining, you are given bonus XP for each
one. Checkpoint Resets are available only in single-player. In Online Multiplayer Racing, Resets are
just a convenient way to get your car back on the road if you get stuck or want to avoid a wreck, but
they won’t help you win!
