Given this scenario, it doesnt matter what type of plane I was flying. Most airplanes are limited to 10 kts tailwind and this is my personal limitation (even if the runway is 12000 feet long) Adding that this is at night, it is not known from this example whether or not the other side has rising terrain or not. I have lived this long by not making a lot of assumptions in order to bend scenarios to work to my liking. My experience is that if there isnt a VASI or an approach to a runway, there is a reason. Think "Big Picture". We should all be able to make an approach at night without vertical guidance, however unless we know exactly what terrain or obstacles are on that side of the airport then we should err on the conservative side.
In fact the practice of building approaches in the FMS should only be used for secondary guidance and not a primary means of vertical guidance.
I'd say wait for the winds to die down and start looking at other airports to divert. Your boss might call you a pansy but you wont be playing russian roulette with his fancy plane.