You don’t “rewrite” any Constitutional amendment, you propose another that acts on it and put your proposal up for a vote in Congress and then a ratification by the states. The difficulty the gun control fanatics have encountered is that every time this issue does go to ballot, they lose.
You have just explained why the Article II, Section 1, clause 5 eligibility requirement to be President, ‘Natural born Citizen’, hasn’t been amended.
Once the explanation is widely understood - a Natural born Citizen is born in the United States of citizen parents - there will be few if any dissenting votes.