The GWB is do-able very early on a Sunday morning IMO. It may save you time/miles on both sides.
At other times . . . joining the chorus for the Tappan Zee to I-287 and I-95.
BTW using EZ Pass will save you a lot on tolls. Here is the NYS form to get one to include your two-axle AS:
https://www.thruway.ny.gov/ezpass/ta-w68176.pdf
The NJ DMV may have its own rules/forms. If you already have an EZ Pass account, a simple phone call may get the correct tag mailed you.
Good luck,
Peter