You have enough hot pixels that it may be confusing to the auto-removing algorithm so that it thinks they are data, maybe?
In the Develop module, Details panel, Noise Reduction, "color" slider, see if a setting of 15 helps you out. Experiment as necessary, but too high may affect the star trails.
Thanks for the reply! The Color slider was already on 25, and changing it to be more or less didn't seem to have any effect on the dots.
Even though that is not the purpose of the Color slider, I thought it might be worth a try.
In this case something like what Nikon calls "long exposure noise reduction" might help you, if your camera has it, where a dark image of the same exposure time is subtracted from the original image to remove the stuck pixels and heat blooms, etc. However, that might also leave some gaps in your star trails.