No matter how much you tweak the properties of the spotlight sun to solve one problem or another, you will always create more problems than you solve. You can solve the 6 hour daylight problem, but in so doing you fail to make the poles have six months of daylight, followed by six months of night.
And even if you decide you will give unfathomable intelligence to the sun so it illuminates just the right places, just at the correct moment, you would still have no solution whatsoever to the problem of having the sun showing the same apparent size and luminosity on every part of the Earth, and showing the same sunspots to every place on Earth.
In short, a bad idea will not become a good one just because you want it to.