Just find the least populated instance and work on the missions there. I completed the PVP missions on three characters back to back the past couple nights and can count on one hand the number of players I saw in the PVP area. There was only one time another player approached within 30m and that was because they had an orb to turn in as well and likely didn't feel like taking a chance fighting.
I really think that lots of players having an issue with this are likely bringing the grief on themselves. If the area is too hot, wave off and come back later. If you get killed, shrug it off and come back later.