The time of day is when I want it.
Not sure I understand this. I was not suggesting to change the time of day, just a few minutes, or perhaps even one minute earlier.
Star effect? Could you please explain??
You can find an explanation and examples of so-called sunstars here
. If that is not what you want, and you do not want to shoot even a minute earlier, than I am afraid you would have to live with the ugly digital rendering of the sun, as others already pointed out. Or you can shoot film, use a prime lens known for a good flare rendering (though that only tackles the lens side of the problem, not the sensor side), or use post-processing to mitigate the effect (blurring the area around the sun, using negative Clarity, etc.)
Here is my example of a sunstar (sorry for the bad transparency scan, but just wanted to show the star effect):
P.S. Ah, yes, that was film, prime lens (Zeiss Distagon CF 50/4 for Hasselblad), f/22... any halo still visible is actually a result of (bad) scanning, not on film