James,
About 4 feet away - I didn't measure. I'd just come back from some mola dives, hadn't used much of the card - too much work uphill finning to do much shooting. The camera and housing were set up, and there was still enough light for the autofocus to work, so I dropped into the pool with mask and snorkel and took a few shots of the with the zoom cranked all the way in to 12 and all the way out to 24.
I wasn't worrying much about focus, as long as the shot was clear enough to show the extent of rectilinear distortion, and aligned close enough to true horizontal that I could reproduce the image aligned and as close to full frame as possible, without a lot of rotating and cropping. Also, I was shooting at 1/30 (no strobe, to avoid strobe reflections off the tiles, late afternoon). I suspect the softness in focus is more a matter of camera movement at the slow shutter speed. I don't think there is any problem with close focus using this lens, dome and diopter configuration at much closer distances than this. (See image below.)
But the 2X diopter was of course still on the lens from the dive. My position is that, with this dome, this diopter should be on the lens at all times.
The comparison between the pincushion problems so dramatically evident in Craig's tile tests vs. mine suggests that the Subal FE2 dome, in combination with the 50 mm extension ring, may work better with the 12-24 lens than the configuration Craig used, which I infer was the Nexus 170 mm dome plus 25 mm extension ring, no diopter. But it's not clear to me whether the problem with Craig's test shots is primarily related to the dome optics, size of extension ring (i.e., alignment with lens nodal point), presence/absence and/or choice of diopter, or some combination of the above.
In any event, I feel even more confident now that the Lee Paterson/Al Burton conclusion (that "the design of the 12-24 AF-S lens precludes the use of optics in front of the lens" due to unacceptable pincushion distortion") on the MCD website page Craig cited can be dismissed out of hand. My test pictures were taken with a +2 diopter.
The discrepancy can probably be attributed to the fact that Paterson and Burton tested the 12-24 with the Subal SWB dome, which is not suitable for any lens this wide. Subal's position, I believe, is that the only the FE2 dome (on a Subal rig) can be used with the 12-24 and other super-wide (< 18 mm) lenses.

Image taken with 12-24 zoom lens at a distance of about 2.5 feet (from the barrel sponge).