I guess that Nvidia Geforce cards will not solve your problems, it probably makes your situation more frustrating...
Geforce cards do not allow you to set ID on the Outputs. The number of connected outputs are defined from Windows. Once you have reboot your PC, you struggle with putting correct output destinations to the correct projectors. After every reboot Windows will put your projector by random numbering.
The only solution in my mind is using a Quadro card oder Matrox, Advoli. There you can define exact each output destinations as well you can set the EDID manually. Those functionality are only available with professional graphic card or I am wrong?
Propably thats the reason why you are using P4000 cards and not more powerful and cheaper Geforce cards!?
Have you done any tests with a quadro P5000 cards? I know cost more than a car...
We made some tests with an 6x HDBaseT card (advoli). We got a good frame rate although we saw stuttering in the videos. The stutter at 60fps was by far not so bad as it is with a P4000 with 4 outputs.