I would like to point out one thing as well:
I believe even if you master adding such a small nuances to your Japanese I don’t think natives will notice it. They will probably assume you don’t get the difference if you will try to use less common one in given situation to add nuance.
Look at this this way:
I know there is a difference between “must” and “have to” but I know it is so small that there is not point in bothering. Do you think if I would use “have to” in situation that “must” make more sense to add some nuance, you would assume I tried to communicate something extra? I don’t think so. I just made a few mistakes. You will assume it is just another one.