Actually whilst I was in the build and research stage of this little probe I had an ilumination

about the grey shade required for a starting point.
The light at the black point and lower(<16 black) on any of our projectors is known as light bleed. Ths light is actually quite strong and very measurable with a LUX meter. This is the issue we might need to attend to before thinking about ambient light. My thinking is to look at how much light there is at below black, this will be different for everyone and with that figure work out how grey you would need to absord this light that is not wanted.
My projector has 25lux at the reference point of black which is known as 00IRE in the grey scale. At white(100IRE) of the grey scale I have 677lux. Throughout this scale (although I'm guessing this point) I assume that I have this extra 25lux that exists as light bleed.
So my starting point would be a surface that absorbs the 25lux, or as much of it as possible that doesn't kill the white level point.
Looking at some grey neutrals avaliable to me and working with the 25lux as a value.
Black(00IRE)=25 lux
N9 229 rv82=20.5 lux
N8 202 rv65=16.25 lux
N7 175 rv51=12.75 lux
N6 149 rv36=9 lux
Remember light works in log and is non linear. Like sound every drop in 3db volume is percieved as a halving of volume to us, luminance works the same way.
Dropping to N7 may infact be too much for your projector to give you a bright picture anymore because it would absorb 49% of the whole, 677 lux would be 345.27 lux at white. As previous experiments have shown with enough spare lux one can use black as the reflected surface, ie if i could get 650lux returning from the reflection on a black surface I would see a bright picture with deep blacks.
Obviously not possible unless my screen was 1 foot in size.
Leaves us around N9 229~N8 202 for your low lum projector and for any light cannons you could go down to N7 175.
All depends on you projector spec, lum output, screen size, light bleed value and finially any ambient light.

Prof, with enough head room in the projector adjustments you could tweak out a projector/screen calibration of a color push. But frankly most don't have enough range before they start clipping. You might cope with some of the grey scale, but the top and bottom would/could clip. I have heard comments about some of the mixes and skin tones but then colors seeeming right in other areas. This means the screen is doing odd things. pushing or pulling points of color balance will do odd things in other areas. Bit like pushing in on a balloon.
I am new and a complete novice at this calibration thing, so far I have found you have to balance a number of different aspects not just RGB balance.
The probe s that work with the HCFR software.
DIY HCFR probe(designed too)
DTP94
spyder2 ( I have at hand(borrowed) a Spyer2pro and this so far has not worked because of different dll files)
It works by taking light readings, no matter what the source. SO the light source is an issue. You can actually get the DIY sensor as a mounted kit for measuring test cards, surfaces etc. Around about $90us. Not sure about the software, haven't looked into it.
The DIY sensors have an array of clear, red, green and blue photo receivers and is tiny. The spyder and DTP94 use an array of one type of detectors with filters.
There is arguments about which is more accurate. All are accurate enough for us.
Although the DIY really needs an IR filter to eliminate interference, when that is done it appears to have an edge on the other types of probes.