I recently acquired a Think Tank Shape Shifter, which is specifically made to hold the three "Trinity*" zoom lenses and two pro-sized camera bodies, in neoprene pockets, and a large (17-inch) laptop. The bellows-type construction allows the body of the pack to be zipped to assume a much thinner front-to-back profile when the cameras and lenses are not inside the pack. The Shape Shifter is not intended to hold many general items other than those listed, so one's luggage would need to be carried elsewhere.
As the OP's narrative indicated a road-trip tour, this brought to mind that a tour bus would be the mode of transportation, and while I have not (yet) traveled by tour bus, I would think the Shape Shift might be well-suited, based upon the OP's specified equipment, particularly the three fairly large lenses.
I must emphasize, however, that the Shape Shifter is a specialized backpack, best suited to those who are carrying the equipment for which it was designed to carry, three pro zoom lenses and two bodies, in the designated neoprene pockets, or other items that will fit into those pocket sizes, such as substituting Speedlights for a body or lens. (Obviously, a pocket sized for a pro DSLR body can hold quite a bit.) A visit to Think Tank's site would be a good idea; personal inspection would be better. All of their products seem very well-designed; something else in their line-up may be better-suited.
I had the advantage of personally inspecting the Shape Shifter at Houston Camera Exchange before buying. (HCE stocks much of the Think Tank line-up. HCE does not sell on-line, except for some few items, mostly clearance, listed in their Ebay store.)
I should emphasize that I am not a representative for any manufacturer or seller, and receive no compensation or dividends for promoting anything. I am a satisfied customer of HCE and Think Tank, and strongly believe in supporting my local independent pro-level camera store.
*The "Trinity" pro zooms are the Nikkor 14-24/2.8G, 24-70/2.8G, and 70-200/2.8G, and the Canon 16-35/2.8L, 24-70/2.8L, and 70-200/2.8L.