I love this question and I'm totally stealing it to use as an example for my practical board repair workshop!
The deal here is definitely long screw trace damage, which in the iPhone 6, will take out the backlight. My guess is that your phone DOES power on--i.e. it can be detected in iTunes, and what you are describing is no backlight, not no power.
Even better is that I believe that the missing screw bracket is also a red herring---but I could be wrong about that. My guess is that you will have trace damage under all the screw brackets since we know that you did mix up the screws and I can see screws that are screwed into all the other brackets without the LCD shield---which will make all the screws too long for the brackets and therefore pressing into the board.
I have fixed a few of these---I see that you asked for a quote on my iPad Rehab website so I will answer you there.
For anyone else reading this----get your iPhone 6 screens done at Apple for $109+ tax and avoid these kinds of problems
Update: Great news for you Blake---it was trace damage and I was able to repair it.