I swear by my life and love of it that I will never live for the sake of another man, nor ask another man to live for mine.

This is a recurring topic. Other people have started similar discussions. Here are two that I began:
Book Review: The Constitution of Government in Galt's Gulch by Wolf Devoon
http://www.galtsgulchonline.com/posts/9f...

Contradiction in the U.S. Constitution
http://www.galtsgulchonline.com/posts/95...

As you can see from Devoon's book many other people have addressed this over the years. The discussion about problems in our own federal document highlight some of the things you might want to consider when outlining your ideas for a better arrangement.

db wrote an interesting article where he came up with a Regulatory Bill of Rights. see here: http://hallingblog.com/regulatory-bill-o...
Concepts such as three branches of govt, rules on Vetoes, whether the Supreme Court has the final say on constitutionality, whether we should have a Constitution that divides powers between states and Federal, etc. All of these are procedural and practical legal questions. They are designed to protect our rights but they do not logical follow from our definition of Natural rights.

This is a fun Q for me from the outside,
surely, it is a fundamental flaw to have three arms, when there should be two?

The correct role for a head of state is to greet visitors, inspire, to be respected, to be a role model, and to sign off on legislation.
Impossible if the same person is politically active.
Instead, somehow, the public have allowed, or the supreme court or the constitution allows, the head of state not only to initiate law, but make it via executive decision thereby obviating the essential purpose of the legislature.

The solution could be to abolish the legislature and give the president more staff to write laws, thus an elected dictatorship, but better, restrict the head of state to powers as that of Europe's constitutional monarchies, and say like the presidents of Switzerland, Germany and Singapore as described above. Government departments do not report to the head of state but to elected positions. The household of the president/sovereign may or may not have a big budget for limos, yachts, entertainment, parties and interior furnishings, but they make no laws.

I understand that when Britain's Queen Elizabeth II was young, prime ministers were shocked when she did not just sign but asked questions about the proposed new law, intelligent and informed questions. The prime minister was expected to have a good understanding of what they were bringing in, note that the sovereign refusing to sign is unthinkable, but it could mean some hours of exposition. There may be rumors about QE II's politics, but these are not public so she is generally revered and even anti-monarchists respect the person.

Another one not picked up so far is the proposed constitutional point of Rand's Gulch judge, that government shall not restrict trade.