What Vaibronco said is right !
We do all our vertical take-off, it does not matter how high you have to climb, the same way, day or night.
If you do that all time, you just know what you gone see and what the aircraft is doing. 10 degrees nose down 1 second, level off, you know that the airspeed won't show up until you reach 40, with VTOSS, 5 degrees nose up to reach Vy.
We don't have to guess what to do, it is always the same. Now, at night, it is crucial to follow your instrument, there is no other way. We only have NVG's for a 1 1/2 year, I flew 20 years without NVG's doing the same thing with all kind of weather and sites.
Is it easy ? no, it is not and sometimes you really have to concentrate and make sure the guy beside you makes the right calls and check you. The only thing the NVG brings on black hole is to see your reject area, when you rotate, you only look and follow your instruments.
Now, if you never do those profile and try to do it on a black hole, that's a different story, that's gone be difficult to go from 7 degrees nose up to -10 and you will have many risk of being disoriented.
They could have use the Transition up, but I am sure they never even it tried before, you can only do it on a flat surface, from hover, It is a little bit strange because the aircraft vibrate, move slowly initially until you reach enough speed to stabilize everything, departing above water using TU can look scary.
At the end of the day, it is very difficult to say and accept that you are not good enough or not trained enough to do a job, especially on VIP jobs. The only guys who could tell you is your partner (if he understand the situation) and the training guys.
But, it is another problem, we go to CAE and now flight Safety. Who is gone say, " We think you don't have the right level for the job you do". Nobody !!! Most of them don't even understand what we do. " Ho you Canadians, you do all those black hole profiles, it is crazy".Yes, it is but, it is part of the job and we tried over those years to improve those profiles to make them better. Now, with NVG's, we don't have problem to go anywhere as before, but the take-off is still something to manage properly.
All guys who did their training knew what problems those guys had and they should have react. Even you can't know what a customer is gone do with his aircraft, the minimum should focused on aircraft knowledge and management. They should leave the sim with a perfect knowledge of FMS, automation and crew management. Using automation without a perfect knowledge of is happening is a killer, the confusion you get is the best way to have a major mishap.