Very interesting thread and its exactly the same problem I've encountered recently. I've noticed that last two years I was missing a lot information from color point of view when watched Videos.
First of all you should understand (newbies to that) when you choose software players - they use different rendering controls, it could be DirectX rendering control, it could be GPU rendering control, could be anything else, and depending on that factor - result will always be different.
High End projectors designed for movies 2d and 3d mainly, so I won't be clarifying here how to calibrate your projector in order to view PC desktop, i.e. different graphics and etc. For me my main task is how to configure correctly your chain in order to display movies as they should be displayed.
I use MPC-HC + madVR (renderrer), madVR renderer is a unique render across all famous renders provided in our days and is the most GPU effective, as their algorithms allow you to reuse GPU element at its 100%, thus upscaling, sharping and other effects - they performed at best quality. The same relates to Output SIGNAL. I would agree to those who said that option 3 is the best, but I would mark one thing as when using MPC-HC + madVR it doesn't rely on the settings you set in your GPU as how the signal is performed, as madVR uses its own algorithm how to process the signal. This effect will take in place only for Windows Media PLayers as its algorithm are reusing GPU directDraw how signal is processed, in that case it is important that in Video settings of your GPU you set it to RGB Full, as by default it is RGB Limited in every GPU.
Now if you load any movie and use my described method MPC-HC + madVR, set in madVR output signal as PC (0-255) readjust your contrast and brightness accordingly using AVCHD test patterns, preferably to use Misc Patterns -> A - Greyscale where it shows all marks how white should be displayed at 235 level and black should be displayed at 16 (to find out more go https://dl.dropboxusercontent.com/u/...rns-Manual.pdf
refer A2 Greyscale Steps), choose some scene which has a lot details in deep black area, take photo. Now switch in MadVR output signal as TV (16-235) and readjust your contrast and brightness again accordingly and take a picture. You'll notice a big difference that using TV (16-235) provides much more detail of deep black and gray levels, where PC (0-255) will make everything black however you'll notice from previous screenshot that it should contain more details (shades and more detailed picture of dark object). And its not about BTB or WTW effect, this is how it should be displayed and only that way. The only problem is that when you have that chain
MPC-HC/madVR (16-235) -> GPU (doesn't metter what setting as madVR will always overwrite it, you can test it) -> Projector (Input signal Standard i.e. 16-235) it is a bit more difficult to calibrate your projector's gamma to be consistent as my settings of brightness should be set to -23 and contrast to +9 this cause curve of gamma to be inconsistent and I'm still in process to finalize calibration. Despite that small problem video quality is just superb!
Please don't compare anything other than that, when you feed 4k pattern signal generators or use native JVC generators it will be calibrated for playing videos from Blu Players - not PC so playing it from PC won't be the same calibrated result, even with the method I've described above.
I'll probably release youtube video to close a lot of questions with all different tests and results, the only problem it takes so much time - couple of days ago I've spent around 4 hours for two days and I still need more time to fully understand how it all works.