If your grey will step up for you, once you have him on your hand place your other hand over his back and pop into the travel cage. If that won't work, birds do not normally move around in the dark so, darken the room and pick him up and pop him into the travel cage.
On another note, you must see some beautiful country, I am very jealous. Before my late husband passed, we went by motor home across all of the US and into Mexico and Canada. Great experience that I truly enjoyed.