I've only done a one-way R2R, but I would think that if you are carrying overnight gear, there is no way you will succeed in a one-day R2R2R.
Also, the North Rim facilities are scheduled to close on Oct. 15 for the winter, so you might not find any services at the north rim.
I hope others here have more information for you.
Hiking across the Grand Canyon is a fantastic experience. Good Luck!