It would also be fairly obvious that someone was trying to move several thousand pounds of hardware onto the moon, and launch detection satellites would be even more effective at monitoring the moon. So you've got a first strike, that will be detectable basically immediately, and weapons that now need to travel ~385,000 km and survive even more serious re-entry than the ICBM's based on Earth. Or you've got a second strike capability that cost you billions of rubles/dollars.
Once you look at it like that, its pretty easy to see why the submarine launched weapons were the preferred method for threatening rapid first strike while providing a guaranteed second strike capability.
I didn't do the math but at that speed you don't need a warhead to destroy a target. Let's try with 1000 kg steel or whatever won't melt down
1/2 mv^2 = 500 * (3200 * 3600)^2 = 345,500,000,000 J
1 J lifts about 100 g mass by 1 m on the surface of Earth. That energy would lift 345,500,000 kg by 100 m.
The lunar orbit->earth delta-v is 4.8km/s. I didn't check your other numbers but they seem to be off by a factor 1000 too.