Here's a definition of Natural Rights that you might find acceptable:
Natural Rights are the liberties which The Nation's Founders believed could never be surrendered up to the state, and its citizens remain free.
AK
I am having a little trouble extracting a definition from what you wrote. Let me paraphrase and see if I get it right:
Absent a government we all have unlimited liberty.
We choose to allow restriction of some liberties to attain the benefits of a government which (among other things ) referees conflicting pursuit of liberties.
But some of those liberties should never be surrendered under any circumstance because to do would be to surrender freedom.
And those liberties are called rights.
Is this a fair re-statement of your "definition?"