My grandmother lives in Ft. Lee and the drivers for the taxi service she uses (Babe's--the lowest of the low when it comes to quality of product, but they're quite reliable--at least for her and her family, since she's had an active account with them for decades) almost always take the Triboro/RFK rather than the Whitestone to get from Ft. Lee to LGA or JFK.

It's a toss-up between the Harlem River Drive and the Deegan for getting between the GWB and the Triboro. But listen to traffic reports to see which one is worse, and unless you hear something really bad about the either the Grand Central Parkway OR both the Deegan and the Harlem River Dr, I'd take one of the Triboro routes over the Cross Bronx to the Whitestone any day. Either way, you may get stuck on the Van Wyck.