Okay! Got you. Your tonemapped image does contain less noise in the shadows, when one brings them out. (Ignore my previous post if you like .
However, I have to say, if I was converting a RAW file of this image and saw that degree of noise in my rendition below, I'd do another conversion either using luminance smoothing in ACR or noise reduction in RSP. A small adjustment at the conversion stage can have a quite noticeable effect on noise without reducing resolution to any significant degree that can't be compensated for with appropriate sharpening.
The mathematics of lower quantization errors might be clear to you, but this issue won't be resolved for me in practical terms until you can provide a RAW file that will open in ACR and preferrably RSP as well. I don't suppose you could borrow a Canon 5D and take a shot of a particularly contrasty scene, could you?
If we are talking about fewer quantization errors in the shadows, I believe a simple dual conversion in ACR can provide a marginal improvement, but so marginal in my experience, that the added difficulties of getting a good blend without halos does not make that procedure worth the trouble, in my view. But perhaps my skills in PS are not up to the job.
Below are the lower right corners. My image, of course, is the one with less blown highlight area. The noise reduction in your tone-mapped image is significant and I failed to get a similar noise reduction in my image using Neat Image. I suppose one could argue that whatever noise reduction one achieves at the conversion stage, further noise reduction can be achieved with your method. If that's the case, I look forward to using your plu-in .