The fact that your visa will be expired is not really relevant. You can re-enter the US after a trip of less than 30 days to Canada using Automatic Revalidation even if your visa is expired, if you are continuing your program on J-1 status.
So the question is whether you are returning to continue your program in J-1 status. You did not indicate one way or another in your question, but since you mentioned the 30-day grace period, I am assuming that you will have completed your program, because the 30-day grace period is a 30-day period of time in which you remain in status after the completion of your J-1 program.
If you leave the US during your grace period, then that's it. You cannot re-enter into J-1 status to resume your grace period. You can only re-enter into J-1 status if you are continuing with a J-1 program.
Yes, you can always try to re-enter as a visitor on the Visa Waiver Program.