Hi there,
What an interesting question! I never thought about using the same language in different forms as you have written here.
Yes, "Don't get me wrong, ..." does mean about the same as "Don't misunderstand me, ...", but they have slightly different functions I'd say. "Don't get me wrong, ..." is a polite request for the person to please believe the next thing that you say. If you said 'Don't misunderstand me, ..." It sounds a bit more like a direct instruction, and it may even suggest that you think the person will try to misunderstand you.
Compare these examples:
- "Don't get me wrong, I love spending time with your family. It's just that I like to have my own space, you know?" -> Very tentative and considerate.
- "Don't misunderstand me, if I have to spend time with your family then I will and I won't embarrass you, but I don't want to if I don't have to." -> Maybe someone said this in an argument.
So I would say "Don't get me wrong, ..." is more like saying "Please understand that ...".
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Unfortunately the other forms are not used, though it's a nice idea! I could probably understand you if you used these in conversation, but I would not recommend intentionally learning them. It's best to learn these phrases as a whole, don't try to break them down too far.
Interestingly, though, you can say "You've got me all wrong.". This means "You have misunderstood my personality." / "You have somehow gotten an incorrect impression of me." / "That's not what I'm like." etc.
I hope that helps, any questions just ask :)