If your projector is calibrated such that R=G=B produces x=0.314 y=0.351 than the way to get another creative white is to make objects in the content you want to appear neutral have non-equal display code values.
Let's say you have a grayscale that you've deliberately graded to have non-equal display code values because you wan that grayscale to be something other than x=0.314 y=0.351.
At some point the grayscale is going to hit 1 in display code value space in one of the channels and the white point will begin to shift ... Then it will clip in 2 channels ... Eventually all 3 channels will hit 1. That means that point in the grayscale will be x=0.314 y=0.351 because that's what the display calibration dictates.
I think the answer is yes.
I think so ... assuming you're aware of the white point is going to shift back to the display calibration white point once the display code values max out in each channel.
The result should be pretty darn close. The P3-DCI ODT "D60 Sim" operation has a very slight roll off at the top so you don't get that drift I was talking about above, but it means your max luminance out of it will be slight less then the projector max luminance.
(Full disclosure, this is what I believe happened based on piecing together the story over years, but I wasn't around in the early days of digital cinema to say for sure)
I think the reason we're stuck with the green white point is a bit of an "accident" of history.
When they were first developing digital cinema projectors max luminance was an issue and a lot of work went into getting to 14 ftL on screen. Obviously, they measured the luminance at a chromaticity that yielded the most light. That just so happened to be x=0.314 y=0.351.
When the projectors shipped someone built a PCF that was called P3-DCI and used that white point so the maximum possible luminance on screen was achieved. Nowadays getting to 14 ftL isn't an issue, even at a variety of white points but people just know "Hit the P3-DCI button". Likewise, downstream hardware and software that make DCPs out of P3 files pretty much universally assume the white point of those files is DCI so there's a whole ecosystem of tools built around that unfortunate white point.
If you know what you're doing, you can easily modify your pipeline to deal with another white point, but it takes some thought and work.