politics

It is not that difficult to get a case submitted to the Supreme Court. The challenge is getting them to accept it (then to rule in your favor). If they are inclined to overturn precedent, they are likely going to accept a case that involves it.

The SC also has the option to simply overturn it on a random other case. For instance, in Trump v Hawaii, Roberts, writing the majority opinion, wrote:

Finally, the dissent invokes Korematsu v. United States, 323 U. S. 214 (1944). Whatever rhetorical advantage the dissent may see in doing so, Korematsu has nothing to do with this case. ... The dissent’s reference to Korematsu, however, affords this Court the opportunity to make express what is already obvious: Korematsu was gravely wrong the day it was decided, has been overruled in the court of history, and—to be clear—“has no place in law under the Constitution.” 323 U. S., at 248 (Jackson, J., dissenting).

reforming the Court through an amendment

I agree with everything you said, just want to point out that no amendment is needed. The Constitution explicitly grants that right to Congress without requiring non-standard approval such as a supermajority. It would just take a law.

The last overhaul was in 1869, which matched the number of Supreme Court justices with the number of (then) circuit courts. These are now federal district courts, and there are thirteen. I am all for doing the same thing they did in 1869: increasing the number of justices to thirteen to match the current number of district courts.

I been a proponent of moving the US Marshall Service under the Judicial. Give them an enforcement mechanism that isn't reliant on the Executive cooperating. Because they clearly aren't following court orders currently.

This is a really great question! You've already got the underlying reason down too - all the various executive departments were created to distribute the enormous administrative burden of figuring out how to enforce laws that have been passed.

Interestingly, Congress is actually in charge of creating the various departments. The President is not authorized to abolish or create new ones, or to expand their jurisdiction or invent new powers, however they are responsible for proposing leaders to each and soliciting their guidance for topics within their domain. How this currently gets enforced is part of the issue however.

Independent agencies also exist that do not explicitly fall under the authority of the President. While the President can remove heads of departments for any reason, there is a much higher bar for removal of independent agency board members.

As the office of the attorney general is one of the government's oldest, established during the first Congress, this may be a matter of combatting tradition more than anything else! This predates independent agencies by something like 100 years.

I should also edit in a clarification that the DOJ not being an independent agency is what allows it to be more partisan than something like the FTC. Also that an independent agency does not in and of itself entirely mitigate partisan politics from its decision making.

Three branches of government is too few

No, sir, away! A papaya war is on!

they can get the votes by showing six senators evidence of their crimes, and extorting them into choosing between voting and prison. I would prefer they go to prison, but IMHO correcting the serious harm this much presidential power causes is a worthwhile tradeoff.

Alternatively, the next dem president walks into the Senate with a shotgun and tests that immunity ruling.

I would love to see this happen but have little hope. I think Trump's base support would have to completely crater for that many senators to cross him