In your first screen shot, the PS image is a 32bit preview of the HDR file. According to the description of your workflow, you then converted this to a 16bit image, in sRGB, and saved that as a TIFF - that TIFF is presumably what is being displayed in LR?
The two image files are completely different, as the 32bit file in PS is being shown with some screen tone mapping that you set up in the "View > 32bit preview options..." menu item.
It sounds like the basic premise of your musing is that LR and PS are displaying the same image differently, when they should be identical with color management between applications.
To be fair, you need to compare the displayed 32bit TIFF in both applications to see if the screen mapping each application uses is similar (there is no 32bit exposure preview slider in LR - I suppose you need to use the Exposure slider to get the same preview capability in LR). Also, I do not know what LR is doing to 32bit files with the auto-ranging tonal compression at the highlight end.
In any case, this comparison would be interesting (32bit preview in LR and PS) to see if the screen mapped preview is similar. If you open the identical sRGB JPEG in PS and LR, do you see a difference in the rendering? If you do, then there is a problem.
As far as the black and white issue goes, who knows.
kirk