Pushing makes all the difference in the world. I've done this test through regular development times without a push at various exposure and pre-flash levels, the difference is minimal and not worth pursuing, essentially not pushing makes the technique for increased speed useless.
Not to mention that without pushing, your scene dMax is 4 stops of exposure lower in the same scene, everything is simply lower.
Assuming colour print film with normal development gives 7 stops of useable range and assuming you exposed at 12800 then your main exposure would give following because you have underexposed by 4 stops.
Zone 1 = 0
Zone 2 = 0
Zone 3 = 0
Zone 4 = 0
Zone 5 = 1
Zone 6 = 2
Zone 7 = 4
Zone 8 = 8
Zone 9 = 16
Zone 10 = 32
Zone 11 = 64
then you pre-flash. Question is at what EI? 800 or 12800? I don't know cos you don't say.
Assuming it was 800 then you get following (if was at 12800 then it wouldn't register).
Zone 1 = 4
Zone 2 = 4
Zone 3 = 4
Zone 4 = 4
Zone 5 = 5
Zone 6 = 6
Zone 7 = 8
Zone 8 = 12
Zone 9 = 20
Zone 10 = 36
Zone 11 = 68
Then you push development by 4 stops and that gives? I have no idea because I never tried or measured it but it will certainly increase separation between zones steepening the contrast curve. And since we are looking for a 7 stop range we are looking to push the zone 7 value up to around 64 which I guess a 4 development stop push would, possibly even to 128.
This would give something like:
Zone 1 = 68
Zone 2 = 68
Zone 3 = 68
Zone 4 = 68
Zone 5 = 69
Zone 6 = 70
Zone 7 = 72
Zone 8 = 56
Zone 9 = 84
Zone 10 = 100
Zone 11 = 132
This is why me and others are saying a pre-flash can produce muddy shadows (look at the zone 1 to 4 values). Your results don't show that which may mean you pre-flashed at 12800 and/or you are using the 7 stop range from zone 4 to 11 to print your result from the negative.
There's an awful lot of me guessing this is what happened in your result. Too many unknown varaibles(to me) to provide anything precise.
When I say Zone = x and give a scale like the one I give, it refers to exposure, and not what is on the negative, starting at 1 is arbitrary, it just can't be 0 because it will never be 0.
Your scale is wrong for what is on the negative that will be measured in optical density, and it will be 0.3d per stop, and not double for every stop, and every stop of exposure isn't going to be 0.3d increments on the neg.
I've mentioned a few times, the Zone III preflash refers to a speed of 12800, or Zone -1 for box speed if you will.
Let's not argue his results with the zone system. Your whole set of calculations assumes that Athiril printed his negative optically, but I remember him writing elsewhere that a very hybrid process followed the development of these negs before he obtained those images. This doesn't take much away from Athiril's accomplishment, after all he could extract image detail where a neg without preflash had none.
I think 'did you print this optically?' is kind of silly, the ratio of people who use colour film to the ratio of people who also optically print it is much wider than the people who are into photography vs the people who also use colour film to start with.
Regardless the results were scanned on a Fujifilm SP3000, it is essentially 'fixed grade', it is very much like printing and offers density (exposure) and colour balance adjustments just like enlarging does, it does not let you set a black and white point.
The 12800, 3200, and 12800 + preflash samples were scanned the same without density adjustments even iirc, no contrast adjustment etc. Meaning the 12800 + preflash is very similar to the 3200 image, maybe even a little higher in the highlight values, not lower as you would expect.
I also checked it out on a Flextight scan and could not pull any of the missing shadow detail out of the non-preflash shots at all in Photoshop, meaning if I couldn't do that, you certainly would never find it by optically printing it.
My test is the only actual data/evidence/samples I've seen of pre-flashing negatives in my life, anything else I've seen about pre-flashing is just claims and information that is borrowed from someone else's claims and parroted.
That said it should work fine on B&W, after all I had based it on the incredible claims of another author online about pre-flash and pushing Tri-X to very high speed and obtaining detail otherwise not possible, to which I found true on this particular film on my very first test.
His method was to bracket pre-flash a roll only (no image exposure) and develop it at a push time and see the frame that has any density at all is the one to go with, and then use that on the next rol. Mine was to bracket pre-flash along with image exposures and judge it directly on the best looking image, as I thought it still could occur prior to any density increase from pre-flash only pushing up exposure values, or even after with a thicker fog.