How do you propose that be implemented? Do you really expect that a narcissistic candidate like Trump, or even ordinary candidates (and I'll simply say every single one here) would do that?

how could they avoid it.

Won't happen.

And you're right.......it won't.

You do know that by adding to the qualifications for the presidency, that your idea will require an amendment to the Constitution, right? And as stated in the op, it doesn't seem very well fleshed out.

About the first proposal,

1. Who will choose the board of doctors?

2. What happens if a candidate claims that the board is biased against them?

3. What if you feel that the board has been packed with incompetent nutcases and deems a candidate fit for office?

And the second,

4. What if homeland security deems a candidate a threat and they are nominated, or if not nominated by a major party, they run as an independent?

5. What if a candidate deemed as a threat is elected?

6. Do you think that homeland security should be able to nullify an election?

One of the consequences of living in the US is that there are times when we think that the president is detrimental to our norms and institutions and a threat to the rule of law and the Constitution. What should prevent that threat from materializing in this country are the checks and balances of the Constitution given to the other branches of government. If those tools are not being used to prevent a crisis, it is up to we the people to choose those that will check and unruly executive.

This proposal is problematic because there are no objective definitions of either assessment upon which you seek to base a judgment of a presidential candidate.

Now that it has been brought to my attention, I agree it would be unconstitutional. You could still set up the boards and make it a voluntary thing. There is nothing in the constitution that says the candidates have to have a debate, but it has become something that is expected of candidates. If a candidate thinks he has disagreement with the board or homeland security, they could make their case. The findings don't have to be binding. You could find respected professionals to be on a medical board the same as people in the FBI or CIA. In the case of the current president, we have a very good possibility that he was elected while being compromised by the Russian government. It was somewhat speculated by the new media, but it could have had a lot more weight put on it if professionals from the intelligence agencies had a say.