It is possible to change “with little effort”…
A lot of stuff within GW2 and over multiple characters on each account are shared resources. I figure this, by creating a second character and leveling it and going with a different order from your first characters order, it will unlock the order for your initial character as well. My main is 80, completed Order of Whispers, I have been inside the Vigil before and am unable to buy that order’s armor as I am not associated with them. So I have currently been progressing with my second character and doing Vigil to see what happens.