This may not be the answer you're looking for but if it looks good in 32bit, just take a screen shot and work with that. There's no way currently to directly translate 32 to 16 bit, but that is a good idea for a feature.
A screenshot would make the quality and resolution much worse I think. Do you know any way to render a 32 bit image to a common format?
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When viewing a 32 bit image on screen you are not seeing the full tonal range - it can't be displayed on an 8 or 10 bit monitor.
That aside, when you use Image Mode and change from 32bit to 16 bit you should get an HDR toning dialogue.
The nearest to seeing in 16 bit what you see currently see on screen is to choose the toning method "Exposure and Gamma" and set Exposure to 0 and Gamma to 1.0
Note : If you get Camera Raw instead of that dialogue you will need to go to Preferences File Handling and uncheck "Use Adobe Camera Raw to Convert Documents from 32 bit to 16/8 bit
Wow that worked perfectly, thanks!