Ok, result for D500: 274 30-second exposures at ISO1600. This was with an un-chipped 55mm f2.8 AI-S lens attached, so no power use for the lens whatsoever. This was without changing the battery, and the temperature was -16 degrees C. I did open the fridge at the beginning of the test, so the camera was not quite that cold at the beginning, possibly -12?
I must say, this is more than I expected.
With regard to how I overcame the bettery life issue at high-ISO, I shoot most of my astro shots at ISO 400. I can see no negative impact on image quality between shooting at elevated ISO or shooting at 400 and lifting exposure to the same level, and usually I don't, instead I will lift exposure in selected areas, thus the overall image quality may even be slightly better.
The disadvantage is that it is impossible to judge the composition, so the session will always start with a few high-ISO shots.
Thanks so much Peter for carrying out this test. This was somewhat encouraging and gave me something to think about. I might want to repeat this test now with my D7100 to see how it responds in comparison. I have done astro imaging with 30sec exposures (I am usually at one minute) , but I cannot recall how long it lasted on that occasion.
I actually handled both D500 and D7500 bodies without lens, but with my own battery inserted for correct weight in the local store here in Fairbanks yesterday. (They do not use to stock high end models so this was a bit of surprise). Both very nice bodies in their own way, the D500 not as bulky and heavy as I recall from a previous occasion, and has the edge when handling with thick mittens. Both could be handled well with a pair of fleece gloves. When I asked them about the battery in these cold environments, they indicated that battery in the D7500 lasted longer than D500 (not surprising). For astro use, the flip out screen of the D7500 has a little edge over D500 in that it can be pulled out a bit further from the body, as the hinge is attached closer to the bottom (but could also be more fragile). My right angle finder might obstruct the view of both of them though.
Using lower ISO and stretching certainly should be better to avoid blowing out stars and get better star colors, as long as there is no pattern noise lurking at the bottom messing up things like on my D7100 (which is OK at ISO 1600).
One thing that favors D500 is a better Hot Pixel Supression (HPS) algorithm. According to recent analysis,
https://www.dpreview.com/forums/post/61908926 , D500 uses a 24 nearest neighbors algorithm, and while the principle is similar for D7500 (which is somewhat better than D5300) it is based on nearest 8 or 12 same color neighbors,
https://www.cloudynights.com/topic/635441-aa-filter-spatial-filter-and-star-colours/page-3.. Thus D500 will not suffer from the "star eater" syndrome, while D7500 might be slightly affected in that colors of the smallest stars might be off if a high resolution lens is used, typically turning them green. That said, D5300, which is even worse, is the most popular Nikon model for astrophotography.