the Bronx through Edison, NJ. Wondering if I should take the long way around on my trip to VA.

But you'll notice, the closer you get to NJ, the better the roads get....:)

You could go through Brooklyn and across Staten Island to the Jersey Turnpike, but to what effect?
If you're traveling over "peak" hours, no route will be satisfactory. If off hour, then just take the GWB to I-95 South and be done with it.

Tappan Zee to 287 and pick up 95 again in Edison. Extra time and distance versus hammering my car over cratered roads.

It does sound like timing it for off peak travel along that part of 95 would be reasonable. thanks.