Hi Alex,
Sorry for the delay in getting back to you here. Your image is tagged with the standard sRGB profile. Since you like what you see, we can affirm that the image is effectively in the sRGB space (a nice advantage of deep-sky astrophotography: we are not constrained by daylight color rules). So the correct procedure to export the image is embedding the standard sRGB profile—or, if the image is going to be deployed to the web, you can alternatively leave it untagged, since sRGB is the default color space of the web; however this is not recommended nowadays, in general.
You can also convert the image to ProPhoto, if you wish (and obviously, assign the corresponding profile). However, you'll gain nothing by doing this because ProPhoto is much larger than sRGB, and probably much larger also than your monitor's color space. In other words, what you already have restricted by sRGB cannot be improved by spreading it into a larger room such as ProPhoto.
If I assign the image a ProPhoto profile, it immediately has major color shifts.
You have to
convert pixel values to the ProPhoto space, i.e., use the ICCProfileTransformation process instead of AssignICCProfile. If you simply assign the profile, you are cheating the color management system... and it always wins!
monitor profile: Calib 02262019 (which is from a calib device and I've been using it for several months now.)
If you use other applications to browse or view images, including your desktop files manager, make sure that the same profile is being associated with your monitor, either on each application, or at the global system level.
Let me know if you get the desired results by embedding the sRGB profile when you save the image.